How do I solve this?

Question

a function f has the first derivative f'(x)=(x+2)x^2(x-1)^3(x-4)^4

on which interval does the function increase?

for which values of x does the function have a local max and for which a local min?

Answer 1

Hi Kate,

Just use properties of the first derivative.

f is increasing where f'(x) > 0.

f has a local max where f'(x) changes sign from positive to negative.

f has a local min where f'(x) changes sign from negative to positive.