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)# .
