a) 0 < x < 3
b) MN/AB = MC/AC
MN = AB*MC/AC = MC = 3 - x
A(x) = AM*MN = x(3 - x) = 3x - x²
c) A(x) = -(x² - 3x + 9/4) + 9/4 = -(x - 3/2)² + 9/4
d) A(x) a un maximum au point (3/2 ; 9/4)
le maximum de cette aire est 9/4 = 2.25 m²
à la position AM = 1.5 m