Find inflection points of the function

In what intervals is the function increasing?

The graph of g(t) looks like this:

It has a single inflection point at (−1, 0).

We find the critical point by finding g′(x) and equating it to 0

Therefore g′(x) = 0 = (-1 + 2t³)/t²

t = (1/2)^1/3

We can see that the function is increasing for

t > (1/2)^1/3