# How do you determine where the given function #f(x) = (x+3)^(2/3) - 6# is concave up and where it is concave down?

##### 1 Answer

May 1, 2015

In order to investigate concavity, we'll look at the sign of the second derivative.

Notice that

The only place where **might** change sign is at

But clearly the numerator is always negative, and the denominator, being a positive times a 4th power, is always positive.

So

The graph is concave down on

Because of the cusp at

Here's the graph of

graph{(x+3)^(2/3) - 6 [-18.74, 13.3, -15.11, 0.92]}