Question

Is `f(x)=(x+7)(x-2)(x-1)` increasing or decreasing at `x=-1`?

Answer 1

It is increasing if the derivative at `x=-1` is positive and decreasing if the derivative at `x=-1` is negative.

Explanation:

In order to answer this question you need to find `f'(x)`

I would suggest using algebra to simplify the function before taking the derivative. While there are several approaches to take, this is the one I chose in order to easily use the product rule.

`f(x)=(x+7)(x^2-3x+2)`

`f'(x)=1(x^2-3x+2)+(x+7)(2x-3)`
`f'(-1)=1*((-1)^2-3*(-1)+2)+(-1+7)(2*(-1)-3)`
`f'(-1)=7+(-30)=-23`
`f'(-1)<0` therefore the function is decreasing at `x=-1`