Verified answer

Bonjour,

a ) PJ

b ) Aire(MNP) = (a + 3) (-f(a)) / 2 = -(a + 3) (2a² / 9 - 2) / 2 = -(a + 3) (a² - 9) / 9

Aire(MNP) = g(a) = - (a + 3)² (a - 3) / 9

c) g'(a) = - [2(a + 3) (a - 3) + (a + 3)²] / 9 = -(a + 3) (2a - 6 + a + 3) / 9

g'(a) = - (a + 3) (3 a - 3) / 9 = - (a + 3) ( a - 1) / 3

x    | -3          1             3 |

g'(x) |0  +       0       -      |

g(x) |     ↑    32/9    ↓.    |  

L'aire de MNP admet bien un maximum qui est 32/9 = f(1)