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

1 Answer
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]}