Question

F(x)=x^3-x^2-8x+12

Write the values of x for which f'(x)>0

Answer 1

$f(x)=x^3-x^2-8x+12.$

$f'(x)=3x^2-2x-8=(3x+4)(x-2).$

$f'(x)>0$ when $-\infin<x<-\frac{4}{3}$ or $2<x<\infin.$