Question

Решите неравенство: f '(x)>0, f(x)=(4-x)(x+3)²

Answer 1

f`(x)=(4-x)`*(x+3)²+(4-x)*[(x+3)²]1`=-(x+3)²+2(x+3)(4-x)=(x+3)(-x-3+8-2x)=
=(x+3)(5-3x)
(x+3)(5-3x)>0
x=-3  x=5/3
x∈(-3;5/3)