Question

How does the first derivative test differ from the second derivative test?

Answer 1

Since you are asking for the difference, I assume that you are familiar with how each test works. The biggest difference is that the first derivative test always determines whether a function has a local maximum, a local minimum, or neither; however, the second derivative test fails to yield a conclusion when `y''` is zero at a critical value. If that is the case, you will have to apply the first derivative test to draw a conclusion.