# 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

- 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

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

Since this is

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