Question

Is `f(x)=1/x^3-x^3` concave or convex at `x=1`?

Answer 1

Concave up.

Explanation:

First of all get f '' (x). f '(x)= `-3/x^4 -3x^2` and f ''(x) = `12/x^5 -6x`.

At x=1, f ''(x)=6 which f ''(x) >0. That means f(x) is concave up.