cours 14
2.6 MULTIPLICATEURS
DE LAGRANGE
Au dernier cours, nous avons vu
Au dernier cours, nous avons vu
Extremums
Au dernier cours, nous avons vu
Extremums
Test de la dérivée seconde
Au dernier cours, nous avons vu
Extremums
Test de la dérivée seconde Hessien
Aujourd’hui, nous allons voir
Aujourd’hui, nous allons voir
Extremums sur une région bornée
Aujourd’hui, nous allons voir
Extremums sur une région bornée Multiplicateur de Lagrange
Avec les fonctions à une variable, il arrivait parfois qu’on veuille trouver le maximum ou le minimum absolu sur un intervalle.
Avec les fonctions à une variable, il arrivait parfois qu’on veuille trouver le maximum ou le minimum absolu sur un intervalle.
On commence par trouver les extremums relatifs comme
précédemment.
Avec les fonctions à une variable, il arrivait parfois qu’on veuille trouver le maximum ou le minimum absolu sur un intervalle.
On commence par trouver les extremums relatifs comme
précédemment.
Et on compare avec les
points frontière pour trouver la plus grande et la plus
Avec les fonctions à deux variables, c’est un peu la même chose, mais on doit préciser quel type de généralisation d’un intervalle on veut
considérer.
Avec les fonctions à deux variables, c’est un peu la même chose, mais on doit préciser quel type de généralisation d’un intervalle on veut
considérer.
Un ensemble sera dit fermé s’il contient tous ces points frontière.
Avec les fonctions à deux variables, c’est un peu la même chose, mais on doit préciser quel type de généralisation d’un intervalle on veut
considérer.
Un ensemble sera dit fermé s’il contient tous ces points frontière.
(le concept d’ensemble fermé est légèrement plus compliqué que ça, mais nous nous contenterons de cette définition)
Avec les fonctions à deux variables, c’est un peu la même chose, mais on doit préciser quel type de généralisation d’un intervalle on veut
considérer.
Un ensemble sera dit fermé s’il contient tous ces points frontière.
(le concept d’ensemble fermé est légèrement plus compliqué que ça, mais nous nous contenterons de cette définition)
Un ensemble est dit borné s’il existe un nombre tel queA<latexit sha1_base64="(null)">(null)</latexit><latexit sha1_base64="(null)">(null)</latexit><latexit sha1_base64="(null)">(null)</latexit><latexit sha1_base64="(null)">(null)</latexit> r<latexit sha1_base64="(null)">(null)</latexit><latexit sha1_base64="(null)">(null)</latexit><latexit sha1_base64="(null)">(null)</latexit><latexit sha1_base64="(null)">(null)</latexit>
Avec les fonctions à deux variables, c’est un peu la même chose, mais on doit préciser quel type de généralisation d’un intervalle on veut
considérer.
Un ensemble sera dit fermé s’il contient tous ces points frontière.
(le concept d’ensemble fermé est légèrement plus compliqué que ça, mais nous nous contenterons de cette définition)
Un ensemble est dit borné s’il existe un nombre tel queA<latexit sha1_base64="(null)">(null)</latexit><latexit sha1_base64="(null)">(null)</latexit><latexit sha1_base64="(null)">(null)</latexit><latexit sha1_base64="(null)">(null)</latexit> r<latexit sha1_base64="(null)">(null)</latexit><latexit sha1_base64="(null)">(null)</latexit><latexit sha1_base64="(null)">(null)</latexit><latexit sha1_base64="(null)">(null)</latexit>
A ⇢ B = (x, y) 2 R2|x2 + y2 < r
<latexit sha1_base64="(null)">(null)</latexit><latexit sha1_base64="(null)">(null)</latexit><latexit sha1_base64="(null)">(null)</latexit><latexit sha1_base64="(null)">(null)</latexit>
Avec les fonctions à deux variables, c’est un peu la même chose, mais on doit préciser quel type de généralisation d’un intervalle on veut
considérer.
Un ensemble sera dit fermé s’il contient tous ces points frontière.
(le concept d’ensemble fermé est légèrement plus compliqué que ça, mais nous nous contenterons de cette définition)
Un ensemble est dit borné s’il existe un nombre tel queA<latexit sha1_base64="(null)">(null)</latexit><latexit sha1_base64="(null)">(null)</latexit><latexit sha1_base64="(null)">(null)</latexit><latexit sha1_base64="(null)">(null)</latexit> r<latexit sha1_base64="(null)">(null)</latexit><latexit sha1_base64="(null)">(null)</latexit><latexit sha1_base64="(null)">(null)</latexit><latexit sha1_base64="(null)">(null)</latexit>
A ⇢ B = (x, y) 2 R2|x2 + y2 < r
<latexit sha1_base64="(null)">(null)</latexit><latexit sha1_base64="(null)">(null)</latexit><latexit sha1_base64="(null)">(null)</latexit><latexit sha1_base64="(null)">(null)</latexit>
Exemple
Trouver la valeur maximale de f (x, y) = x2 + y2<latexit sha1_base64="JWZAPgTktgF3wKQjqb9E6TRDG2Y=">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</latexit>
Exemple
Trouver la valeur maximale de f (x, y) = x2 + y2<latexit sha1_base64="JWZAPgTktgF3wKQjqb9E6TRDG2Y=">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</latexit>
[1,<latexit sha1_base64="Bo/lOC4hBCkk6rObkk1eetFP6Yk=">AAADC3icjVLLTtxAECwcEl55LIEbFyurSDlEKxsiwRGRC0eQWEBaVsg2Axnhl+wx0rLiE/gHruTKDXHlI/IH4cYnUNMMiARFYSyPa6q72t09HZeprk0Q/BrxXo2+fjM2PjE59fbd+w+t6Y+bddFUieomRVpU23FUq1Tnqmu0SdV2Wakoi1O1FR9+t/atI1XVusg3zKBU/Sw6yPW+TiJDarc12/PDr/5Cf8foTNVymO/vttpBJ5DlPwehA224tVa0brGDPRRI0CCDQg5DnCJCzaeHEAFKcn0MyVVEWuwKJ5iktqGXokdE9pD7AU89x+Y825i1qBP+JeVbUenjMzUF/Spi+zdf7I1Etuy/Yg8lps1twG/sYmVkDX6Q/Z/uwfOlOluLwT6WpAbNmkphbHWJi9JIV2zm/pOqDCOU5Czeo70iTkT50GdfNLXUbnsbif23eFrWnhPn2+DGZalwJFEHj9kP5Q417aX0ckBkuMstcSTCvwfgOdic74QLnWD9W3t5xQ3HOObwCV84AYtYxirW0GU2xzjDOX56p96Fd+ld3bt6I04zgz+Wd30HlnihQg==</latexit> 3] ⇥ [1, 2]
dans le rectangle
Exemple
Trouver la valeur maximale de f (x, y) = x2 + y2<latexit sha1_base64="JWZAPgTktgF3wKQjqb9E6TRDG2Y=">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</latexit>
[1,<latexit sha1_base64="Bo/lOC4hBCkk6rObkk1eetFP6Yk=">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</latexit> 3] ⇥ [1, 2]
dans le rectangle
Exemple
Trouver la valeur maximale de f (x, y) = x2 + y2<latexit sha1_base64="JWZAPgTktgF3wKQjqb9E6TRDG2Y=">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</latexit>
[1,<latexit sha1_base64="Bo/lOC4hBCkk6rObkk1eetFP6Yk=">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</latexit> 3] ⇥ [1, 2]
dans le rectangle
Exemple
Trouver la valeur maximale de f (x, y) = x2 + y2<latexit sha1_base64="JWZAPgTktgF3wKQjqb9E6TRDG2Y=">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</latexit>
[1,<latexit sha1_base64="Bo/lOC4hBCkk6rObkk1eetFP6Yk=">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</latexit> 3] ⇥ [1, 2]
dans le rectangle r<latexit sha1_base64="iLlqqU1RP58PPXe9AxoXJ005l8w=">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</latexit> f = (2x, 2y)
Exemple
Trouver la valeur maximale de f (x, y) = x2 + y2<latexit sha1_base64="JWZAPgTktgF3wKQjqb9E6TRDG2Y=">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</latexit>
[1,<latexit sha1_base64="Bo/lOC4hBCkk6rObkk1eetFP6Yk=">AAADC3icjVLLTtxAECwcEl55LIEbFyurSDlEKxsiwRGRC0eQWEBaVsg2Axnhl+wx0rLiE/gHruTKDXHlI/IH4cYnUNMMiARFYSyPa6q72t09HZeprk0Q/BrxXo2+fjM2PjE59fbd+w+t6Y+bddFUieomRVpU23FUq1Tnqmu0SdV2Wakoi1O1FR9+t/atI1XVusg3zKBU/Sw6yPW+TiJDarc12/PDr/5Cf8foTNVymO/vttpBJ5DlPwehA224tVa0brGDPRRI0CCDQg5DnCJCzaeHEAFKcn0MyVVEWuwKJ5iktqGXokdE9pD7AU89x+Y825i1qBP+JeVbUenjMzUF/Spi+zdf7I1Etuy/Yg8lps1twG/sYmVkDX6Q/Z/uwfOlOluLwT6WpAbNmkphbHWJi9JIV2zm/pOqDCOU5Czeo70iTkT50GdfNLXUbnsbif23eFrWnhPn2+DGZalwJFEHj9kP5Q417aX0ckBkuMstcSTCvwfgOdic74QLnWD9W3t5xQ3HOObwCV84AYtYxirW0GU2xzjDOX56p96Fd+ld3bt6I04zgz+Wd30HlnihQg==</latexit> 3] ⇥ [1, 2]
dans le rectangle r<latexit sha1_base64="iLlqqU1RP58PPXe9AxoXJ005l8w=">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</latexit> f = (2x, 2y)
Le seul point critique
Exemple
Trouver la valeur maximale de f (x, y) = x2 + y2<latexit sha1_base64="JWZAPgTktgF3wKQjqb9E6TRDG2Y=">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</latexit>
[1,<latexit sha1_base64="Bo/lOC4hBCkk6rObkk1eetFP6Yk=">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</latexit> 3] ⇥ [1, 2]
dans le rectangle r<latexit sha1_base64="iLlqqU1RP58PPXe9AxoXJ005l8w=">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</latexit> f = (2x, 2y)
Le seul point critique (0,<latexit sha1_base64="ArioZHqqOoghGJcPi/OG8/U6gW4=">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</latexit> 0) 2/ [1, 3] ⇥ [1, 2]
Exemple
Trouver la valeur maximale de f (x, y) = x2 + y2<latexit sha1_base64="JWZAPgTktgF3wKQjqb9E6TRDG2Y=">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</latexit>
[1,<latexit sha1_base64="Bo/lOC4hBCkk6rObkk1eetFP6Yk=">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</latexit> 3] ⇥ [1, 2]
dans le rectangle r<latexit sha1_base64="iLlqqU1RP58PPXe9AxoXJ005l8w=">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</latexit> f = (2x, 2y)
Le seul point critique (0,<latexit sha1_base64="ArioZHqqOoghGJcPi/OG8/U6gW4=">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</latexit> 0) 2/ [1, 3] ⇥ [1, 2]
Exemple
Trouver la valeur maximale de f (x, y) = x2 + y2<latexit sha1_base64="JWZAPgTktgF3wKQjqb9E6TRDG2Y=">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</latexit>
[1,<latexit sha1_base64="Bo/lOC4hBCkk6rObkk1eetFP6Yk=">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</latexit> 3] ⇥ [1, 2]
dans le rectangle r<latexit sha1_base64="iLlqqU1RP58PPXe9AxoXJ005l8w=">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</latexit> f = (2x, 2y)
Le seul point critique (0,<latexit sha1_base64="ArioZHqqOoghGJcPi/OG8/U6gW4=">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</latexit> 0) 2/ [1, 3] ⇥ [1, 2]
On doit aussi regarder sur la frontière
Exemple
Trouver la valeur maximale de f (x, y) = x2 + y2<latexit sha1_base64="JWZAPgTktgF3wKQjqb9E6TRDG2Y=">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</latexit>
[1,<latexit sha1_base64="Bo/lOC4hBCkk6rObkk1eetFP6Yk=">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</latexit> 3] ⇥ [1, 2]
dans le rectangle
Exemple
Trouver la valeur maximale de f (x, y) = x2 + y2<latexit sha1_base64="JWZAPgTktgF3wKQjqb9E6TRDG2Y=">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</latexit>
[1,<latexit sha1_base64="Bo/lOC4hBCkk6rObkk1eetFP6Yk=">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</latexit> 3] ⇥ [1, 2]
dans le rectangle
x<latexit sha1_base64="2HGZBjIElNiaStoRwwtiS3u16tE=">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</latexit> = 1
Exemple
Trouver la valeur maximale de f (x, y) = x2 + y2<latexit sha1_base64="JWZAPgTktgF3wKQjqb9E6TRDG2Y=">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</latexit>
[1,<latexit sha1_base64="Bo/lOC4hBCkk6rObkk1eetFP6Yk=">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</latexit> 3] ⇥ [1, 2]
dans le rectangle
x<latexit sha1_base64="2HGZBjIElNiaStoRwwtiS3u16tE=">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</latexit> = 1 y<latexit sha1_base64="XciUfyG+AUC5HcA82jBL1UaWyX4=">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</latexit> = 1
Exemple
Trouver la valeur maximale de f (x, y) = x2 + y2<latexit sha1_base64="JWZAPgTktgF3wKQjqb9E6TRDG2Y=">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</latexit>
[1,<latexit sha1_base64="Bo/lOC4hBCkk6rObkk1eetFP6Yk=">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</latexit> 3] ⇥ [1, 2]
dans le rectangle
x<latexit sha1_base64="2HGZBjIElNiaStoRwwtiS3u16tE=">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</latexit> = 1
x<latexit sha1_base64="/gbhdTRUYH6WDhLh6D3AwbwxJQ0=">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</latexit> = 3
y<latexit sha1_base64="XciUfyG+AUC5HcA82jBL1UaWyX4=">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</latexit> = 1
Exemple
Trouver la valeur maximale de f (x, y) = x2 + y2<latexit sha1_base64="JWZAPgTktgF3wKQjqb9E6TRDG2Y=">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</latexit>
[1,<latexit sha1_base64="Bo/lOC4hBCkk6rObkk1eetFP6Yk=">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</latexit> 3] ⇥ [1, 2]
dans le rectangle
x<latexit sha1_base64="2HGZBjIElNiaStoRwwtiS3u16tE=">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</latexit> = 1 y<latexit sha1_base64="XciUfyG+AUC5HcA82jBL1UaWyX4=">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</latexit> = 1
y = 2
Exemple
Trouver la valeur maximale de f (x, y) = x2 + y2<latexit sha1_base64="JWZAPgTktgF3wKQjqb9E6TRDG2Y=">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</latexit>
[1,<latexit sha1_base64="Bo/lOC4hBCkk6rObkk1eetFP6Yk=">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</latexit> 3] ⇥ [1, 2]
dans le rectangle x<latexit sha1_base64="2HGZBjIElNiaStoRwwtiS3u16tE=">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</latexit> = 1
x<latexit sha1_base64="/gbhdTRUYH6WDhLh6D3AwbwxJQ0=">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</latexit> = 3
y = 1
<latexit sha1_base64="XciUfyG+AUC5HcA82jBL1UaWyX4=">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</latexit>
y = 2
<latexit sha1_base64="kQcg/ch0xdVy1wewEHAYoOcuTpU=">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</latexit>
Exemple
Trouver la valeur maximale de f (x, y) = x2 + y2<latexit sha1_base64="JWZAPgTktgF3wKQjqb9E6TRDG2Y=">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</latexit>
[1,<latexit sha1_base64="Bo/lOC4hBCkk6rObkk1eetFP6Yk=">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</latexit> 3] ⇥ [1, 2]
dans le rectangle x<latexit sha1_base64="2HGZBjIElNiaStoRwwtiS3u16tE=">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</latexit> = 1
x<latexit sha1_base64="/gbhdTRUYH6WDhLh6D3AwbwxJQ0=">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</latexit> = 3
y = 1
<latexit sha1_base64="XciUfyG+AUC5HcA82jBL1UaWyX4=">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</latexit>
y = 2
<latexit sha1_base64="kQcg/ch0xdVy1wewEHAYoOcuTpU=">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</latexit>
z<latexit sha1_base64="aKqMe4y5U66vHNuESQwXGiW0lxM=">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</latexit> = 1 + y2
Exemple
Trouver la valeur maximale de f (x, y) = x2 + y2<latexit sha1_base64="JWZAPgTktgF3wKQjqb9E6TRDG2Y=">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</latexit>
[1,<latexit sha1_base64="Bo/lOC4hBCkk6rObkk1eetFP6Yk=">AAADC3icjVLLTtxAECwcEl55LIEbFyurSDlEKxsiwRGRC0eQWEBaVsg2Axnhl+wx0rLiE/gHruTKDXHlI/IH4cYnUNMMiARFYSyPa6q72t09HZeprk0Q/BrxXo2+fjM2PjE59fbd+w+t6Y+bddFUieomRVpU23FUq1Tnqmu0SdV2Wakoi1O1FR9+t/atI1XVusg3zKBU/Sw6yPW+TiJDarc12/PDr/5Cf8foTNVymO/vttpBJ5DlPwehA224tVa0brGDPRRI0CCDQg5DnCJCzaeHEAFKcn0MyVVEWuwKJ5iktqGXokdE9pD7AU89x+Y825i1qBP+JeVbUenjMzUF/Spi+zdf7I1Etuy/Yg8lps1twG/sYmVkDX6Q/Z/uwfOlOluLwT6WpAbNmkphbHWJi9JIV2zm/pOqDCOU5Czeo70iTkT50GdfNLXUbnsbif23eFrWnhPn2+DGZalwJFEHj9kP5Q417aX0ckBkuMstcSTCvwfgOdic74QLnWD9W3t5xQ3HOObwCV84AYtYxirW0GU2xzjDOX56p96Fd+ld3bt6I04zgz+Wd30HlnihQg==</latexit> 3] ⇥ [1, 2]
dans le rectangle x<latexit sha1_base64="2HGZBjIElNiaStoRwwtiS3u16tE=">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</latexit> = 1
x<latexit sha1_base64="/gbhdTRUYH6WDhLh6D3AwbwxJQ0=">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</latexit> = 3
y = 1
<latexit sha1_base64="XciUfyG+AUC5HcA82jBL1UaWyX4=">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</latexit>
y = 2
<latexit sha1_base64="kQcg/ch0xdVy1wewEHAYoOcuTpU=">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</latexit>
z<latexit sha1_base64="aKqMe4y5U66vHNuESQwXGiW0lxM=">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</latexit> = 1 + y2
Exemple
Trouver la valeur maximale de f (x, y) = x2 + y2<latexit sha1_base64="JWZAPgTktgF3wKQjqb9E6TRDG2Y=">AAADB3icjVJNT9RQFD0UVD5EKyzZNE5MMJpJZzSBjQmBjUtIGCBBIG15Ay/TaZv2dUIz8Qf4H9zKlh1x68/wH+iOn8B51wdRicHX9PW8c++5vfe+GxeprkwYfp/wJqcePHw0PTM793j+yVP/2cJOlddlonpJnublXhxVKtWZ6hltUrVXlCoaxqnajQcb1r47UmWl82zbNIU6GEYnme7rJDKkjny/v3z2OmhevgvODruvmsPukd8K26Gs4C7oONCCW5u5f4UPOEaOBDWGUMhgiFNEqPjso4MQBbkDjMmVRFrsCh8xS21NL0WPiOyA+wlP+47NeLYxK1En/EvKt6QywAtqcvqVxPZvgdhriWzZf8UeS0ybW8Nv7GINyRqckr1Pd+P5vzpbi0Efq1KDZk2FMLa6xEWppSs28+C3qgwjFOQsPqa9JE5EedPnQDSV1G57G4n9h3ha1p4T51vjp8tSYSRRm9vsx3KHmvZCetkQGe5ySxyJzt8DcBfsdNudN+1w621rbd0NxzSW8BzLnIAVrOE9NtFjNiN8xhece5+8C+/S+/rL1ZtwmkX8sbxv11j+oBo=</latexit>
[1,<latexit sha1_base64="Bo/lOC4hBCkk6rObkk1eetFP6Yk=">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</latexit> 3] ⇥ [1, 2]
dans le rectangle x<latexit sha1_base64="2HGZBjIElNiaStoRwwtiS3u16tE=">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</latexit> = 1
x<latexit sha1_base64="/gbhdTRUYH6WDhLh6D3AwbwxJQ0=">AAAC+HicjVLBbtNAEH01LU1LgQBHLlYjpJ4ih1Sil0oRvXBMVdJWKhWynW26imNb9jqqifiEXtsrN8S1f8MftLd+Qt8OWwRECNby+u2beeOZ2YnyRJcmCL4veA8Wlx4uN1ZWH609fvK0+ez5fplVRawGcZZkxWEUlirRqRoYbRJ1mBcqnESJOojGO9Z+MFVFqbP0valzdTwJR6k+0XFoSO2dbXc/NltBO5Dlz4OOAy241c+at/iAITLEqDCBQgpDnCBEyecIHQTIyR1jRq4g0mJX+IxVait6KXqEZMfcRzwdOTbl2cYsRR3zLwnfgkofr6jJ6FcQ27/5Yq8ksmX/FnsmMW1uNb+RizUha3BK9l+6e8//1dlaDE6wJTVo1pQLY6uLXZRKumIz93+pyjBCTs7iIe0FcSzK+z77oimldtvbUOzX4mlZe46db4Ubl6XCVKLWP7OfyR1q2nPpZU1kuMstcSQ6fw7APNh/3e5028HuZqv31g1HAy+xjg1OwBv08A59DJjNCOe4wKX3yfviffW+/XD1FpzmBX5b3tUdUtmbwg==</latexit> = 3
y = 1
<latexit sha1_base64="XciUfyG+AUC5HcA82jBL1UaWyX4=">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</latexit>
y = 2
<latexit sha1_base64="kQcg/ch0xdVy1wewEHAYoOcuTpU=">AAAC+HicjVLLTtxAECwMhGeSDRy5WKyQOK28BIlckFBy4QiCBSRAkW2GzQivbdnjlcyKT8g1uXJDXPkb/gBufAI1zYB4CCVjeVxT3dXu7ukoT3RpguB6yBseGf0wNj4xOTX98dPnxpeZnTKrilh14izJir0oLFWiU9Ux2iRqLy9U2IsStRud/LD23b4qSp2l26bO1WEv7Kb6WMehIbVVry79bDSDViDLfwvaDjTh1kbWuMMBjpAhRoUeFFIY4gQhSj77aCNATu4QA3IFkRa7whkmqa3opegRkj3h3uVp37EpzzZmKeqYf0n4FlT6WKAmo19BbP/mi72SyJZ9L/ZAYtrcan4jF6tH1uAX2X/pHj3/V2drMTjGN6lBs6ZcGFtd7KJU0hWbuf+sKsMIOTmLj2gviGNRPvbZF00ptdvehmK/EU/L2nPsfCvcuiwV+hK1fsp+IHeoac+llzWR4S63xJFovx6At2BnqdX+2go2l5tr391wjGMO81jkBKxgDevYQIfZdPEbf/DXO/XOvQvv8sHVG3KaWbxY3tU9Utubwg==</latexit>
z<latexit sha1_base64="aKqMe4y5U66vHNuESQwXGiW0lxM=">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</latexit> = 1 + y2
z<latexit sha1_base64="f4sHhyYu1a+IrxLefRGWW/ZXVno=">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</latexit> = 9 + y2
Exemple
Trouver la valeur maximale de f (x, y) = x2 + y2<latexit sha1_base64="JWZAPgTktgF3wKQjqb9E6TRDG2Y=">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</latexit>
[1,<latexit sha1_base64="Bo/lOC4hBCkk6rObkk1eetFP6Yk=">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</latexit> 3] ⇥ [1, 2]
dans le rectangle x<latexit sha1_base64="2HGZBjIElNiaStoRwwtiS3u16tE=">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</latexit> = 1
x<latexit sha1_base64="/gbhdTRUYH6WDhLh6D3AwbwxJQ0=">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</latexit> = 3
y = 1
<latexit sha1_base64="XciUfyG+AUC5HcA82jBL1UaWyX4=">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</latexit>
y = 2
<latexit sha1_base64="kQcg/ch0xdVy1wewEHAYoOcuTpU=">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</latexit>
z<latexit sha1_base64="aKqMe4y5U66vHNuESQwXGiW0lxM=">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</latexit> = 1 + y2
z<latexit sha1_base64="f4sHhyYu1a+IrxLefRGWW/ZXVno=">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</latexit> = 9 + y2
Exemple
Trouver la valeur maximale de f (x, y) = x2 + y2<latexit sha1_base64="JWZAPgTktgF3wKQjqb9E6TRDG2Y=">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</latexit>
[1,<latexit sha1_base64="Bo/lOC4hBCkk6rObkk1eetFP6Yk=">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</latexit> 3] ⇥ [1, 2]
dans le rectangle x<latexit sha1_base64="2HGZBjIElNiaStoRwwtiS3u16tE=">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</latexit> = 1
x<latexit sha1_base64="/gbhdTRUYH6WDhLh6D3AwbwxJQ0=">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</latexit> = 3
y = 1
<latexit sha1_base64="XciUfyG+AUC5HcA82jBL1UaWyX4=">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</latexit>
y = 2
<latexit sha1_base64="kQcg/ch0xdVy1wewEHAYoOcuTpU=">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</latexit>
z<latexit sha1_base64="aKqMe4y5U66vHNuESQwXGiW0lxM=">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</latexit> = 1 + y2
z<latexit sha1_base64="f4sHhyYu1a+IrxLefRGWW/ZXVno=">AAAC/HicjVJLS8NAEP4aX7W+qh69BIsgCCVVQT0IohePFWwr+CKJqy6mSUg2Qiz6H7zq1Zt49b/4D/TmT3B23IoPRDdk8+03801mZseLA5kqx3kqWD29ff0DxcHS0PDI6Fh5fKKZRlnii4YfBVGy47mpCGQoGkqqQOzEiXDbXiBa3tmGtrfORZLKKNxWeSz22+5JKI+l7yqiWherK3P5wfxhueJUHV72T1AzoAKz6lH5FXs4QgQfGdoQCKEIB3CR0rOLGhzExO2jQ1xCSLJd4BIl0mbkJcjDJfaM9hM67Ro2pLOOmbLap78E9CaktDFDmoj8EsL6bzbbM46s2d9idzimzi2nr2ditYlVOCX2L13X8786XYvCMZa5Bkk1xczo6nwTJeOu6MztT1UpihATp/ER2RPCPiu7fbZZk3Lturcu25/ZU7P67BvfDC8mS4Fzjpp/ZN/hO5Rkj7mXOSFFO98SjUTt+wD8BM35am2h6mwtVtbWzXAUMYVpzNIELGENm6ijwX25xg1urSvrzrq3Ht5drYLRTOLLsh7fABzGnSY=</latexit> = 9 + y2
z<latexit sha1_base64="7Qa6SOGbzveE1e1ngflOwgGSfSA=">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</latexit> = x2 + 1