Recall that the Second Derivative Test for Local Extreme (Section 3.3) does not apply when f(c) =

Question:

Recall that the Second Derivative Test for Local Extreme (Section 3.3) does not apply when f"(c) = 0. Prove the following generalization, which may help determine a maximum or a minimum when f"(c) = 0. Suppose that
f'(c) = f"(c) = f"(c) = .... = f(n) (c) = 0
Where n is odd and f(n+1) (x) is continuous near c.
1. If f(n+1) (c) < 0, then f(c) is a local maximum value.
2. If f(n+1) (c) > 0, then f(c) is a local minimum value.