# For what values of x is #f(x)= 24x^3-12x # concave or convex?

##### 1 Answer

Mar 28, 2016

Convex on

#### Explanation:

The concavity and convexity of a function are determined by the sign (positive or negative) of a function's second derivative.

Hence, to determine when a specific function is concave or convex, we first must find its second derivative.

Through the power rule, we see that

#f(x)=24x^3-12x#

#f'(x)=72x^2-12#

#f''(x)=144x#

We can clearly see in

In order to apply concavity/convexity, use the definitions:

#f(x)# is convex when#f''(x)>0# .#f(x)# is concave when#f''(x)<0# .

Thus,

#f(x)# is convex on#(0,oo)# .#f(x)# is concave on#(-oo,0)# .