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

1 Answer
Jan 9, 2016

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