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 x=9/4. If the value is positive, then the function is convex. If it's negative, the function is concave at that point.

To find the function's second derivative, recall that 3/x=3x^-1 and then apply the power rule.

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

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

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

The value of the second derivative at x=9/4 is

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

This could be simplified, but it is evidently positive. Thus the function is convex at x=9/4.