The second derivative test is easy to apply once you have found the second derivative, but unfortunately it does not always work. The first derivative test works more often, but is harder to apply. Let's compare the two tests by investigating the graphs of
Use the first derivative test to investigate the behavior of
, , and at the origin.
Try to confirm your part (a) results using the second derivative test. When does the test work? What can you conclude if you know that the second derivative equals zero at the origin?
The 1st and 2nd derivative tests are ways to tell what is going on at
☛ If the sign changes from negative to positive, then
☛ If the sign changes from positive to negative, then
☛ If the sign does not change, then