Find critical values and critical numbers

In this example problem, we are asked to find all the local extremes for the cube function. To get started, we find the critical values by finding the first derivative and setting it equal to zero. We then solve the equation and get our critical value or number. To create a critical point, we evaluate the original function at the critical number. This is the only potential local extreme but in looking at the graph, we see that it is not a maximum or minimum.