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

1 Answer
Laura
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#

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