# Is #f(x)=-2x^5-3x^4+15x-4# concave or convex at #x=-4#?

##### 1 Answer

Mar 1, 2016

Convex (sometimes called "concave upwards").

#### Explanation:

The concavity and convexity of a function can be determined by examining the sign of a function's second derivative.

- If
#f''(-4)<0# , then#f# is concave at#x=-4# . - If
#f''(-4)>0# , then#f# is convex at#x=-4# .

Note that: you may call concave "concave down" and convex "concave up."

We must find the function's second derivative through the **power rule**:

#f(x)=-2x^5-3x^4+15x-4#

#f'(x)=-10x^4-12x^3+15#

#f''(x)=-40x^3-36x^2#

The value of the second derivative at

#f''(-4)=-40(-4)^3-36(-4)^2=1984#

Since this is