at_answer_text_math
bonjour
at_explanation_text_math
g(x)=x³-16.5x+72x+5
g'(x)=3x²-33x+72
factorisons
3x²-33x+72
Δ=33²-4(72)(3)
Δ=1089-864
Δ=225
√Δ=15
x1=(33+15)/6 x1=48/6 x1=8
x2=(33-15)/6 x2=18/6 x2=3
g'(x)=3(x-3)(x-8)
g'(x)= (3x-9)(x-8)
signe g'(x)
g'(x)=0
3x-9=0 3x=9 x=3
x-8=0 x=8
du signe de a sauf entre les racines
x 2 3 5 (8)
g'x) + -
g(x) croissant décroissant
