# Is #f(x)=3/x-2x# concave or convex at #x=9/4#?

##### 1 Answer

Feb 14, 2016

Convex

#### Explanation:

Find the value of the second derivative at

To find the function's second derivative, recall that

#f(x)=3x^-1-2x#

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

#f''(x)=6x^-3=6/x^3#

The value of the second derivative at

#f''(9/4)=6/(9/4)^3#

This could be simplified, but it is evidently positive. Thus the function is convex at