# Is #f(x)=9x^3+2x^2-2x-2# concave or convex at #x=-1#?

##### 1 Answer

Jan 28, 2016

Concave (this is also called concave down).

#### Explanation:

The concavity or convexity of a function are determined by the sign of the second derivative.

- If
#f''(-1)<0# , then#f(x)# is concave at#x=-1# . - If
#f''(-1)>0# , then#f(x)# is convex at#x=-1# .

Finding the second derivative of the function is a simple application of the power rule.

#f(x)=9x^3+2x^2-2x-2#

#f'(x)=27x^2+4x-2#

#f''(x)=54x+4#

Find the sign of the second derivative at

#f''(-1)=-54+4=-50#

Since this is

graph{9x^3+2x^2-2x-2 [-3, 3, -15, 15]}