Question

How do you find the concavity for `f(x)=3/x^2−4`?

Answer 1

Investigate the sign of the second derivative.

Explanation:

`f(x)=3/x^2−4`

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

`f''(x) = 18/x^4`

`f''` is positive for all `x` in the domain of `f`, so the graph of `f` is concave up on the domain of `f`.

The graph of `f` is concave up on `(-oo,0)` and on `(0,oo)`.