Is #f(x)=(x+1)(x+2)(x-2)# increasing or decreasing at #x=0#?

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Answer 1 · 2016-03-07T18:18:20

It is increasing since #f'(0)# is positive.

First write the function in expanded polynomial form to make differentiating easier.

#f(x)=(x+1)(x+2)(x+3)#

#=(x^2+3x+2)(x+3)#

#=x^3+6x^2+11x+6#

#therefore f'(x)=3x^2+12x+11#

#therefore f'(0)=11#.

Since #f'(0)>0#, it implies that the function #f# is increasing at #x=0#.