Question

Is `f(x)=(x+3)(x-2)(x+4)` increasing or decreasing at `x=-1`?

Answer 1

`f'(-1)=-9<0` so the function is decreasing at `x=-1`

Explanation:

Given `f(x)=(x+3)(x-2)(x+4)`
expanding the Right-Hand side:

`(x+3)(x-2)(x+4)=(x^2+3x-2x-6)(x+4)=(x^2+x-6)(x+4)=x^3+x^2-6x+4x^2+4x-24`

`f'(x)=x^3+5x^2-2x-24`

`f'(x)=3x^2+10x-2`
and

`f'(-1)=3-10-2=-9<0`