Is #f(x)=-3x^3-5x^2-x-1# increasing or decreasing at #x=-2#?

1 Answer
mason m
Feb 9, 2016

Decreasing.

Explanation:

Find the sign of the first derivative at #x=-2:#

  • If #f'(-2)<0#, then #f(x)# is decreasing at #x=-2#.
  • If #f'(-2)>0#, then #f(x)# is increasing at #x=-2#.

To find the derivative of the function, use the power rule.

#f(x)=-3x^3-5x^2-x-1#

#f'(x)=-9x^2-10x-1#

The sign of the derivative at #x=-2# is

#f'(-2)=-9(-2)^2-10(-2)-1=-36+20-1=ul(-17#

Since this is #<0#, the function is decreasing at #x=-2#. We can check a graph of #f(x):#

graph{-3x^3-5x^2-x-1 [-4, 2, -12, 15]}

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