First Derivative Test vs Second Derivative Test for Local Extrema

Key Questions

  • 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.