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Baccalauréat 2009 - Académie de Lille

Epreuve de Discipline Non Linguistique

Mathématiques/Anglais

Thème F : dérivée et optimisation

Sujet 3

L'usage de la calculatrice est autorisé. Temps de préparation: 20 minutes.

Cette planche sera à rendre à l'examinateur, veillez à ne rien écrire dessus.

There are 50 apple trees in an orchard. Each tree produces 800 apples. For each additionnal tree planted in this orchard, the number of apples per tree drops by 10 apples.

1) Fill in the following table Number of

additionnal trees Number of trees Number of apples per tree Total number of apples 0 50 800 40000 1 51 790 2 52 3 53 4 54

2) Let x be the number of additionnal trees, express the total number of apples in terms of x.

3) How many trees should be added to the existing orchard in order to maximise the total number of apples?

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