Use the equation to establish the following test. Let have continuous first and second derivatives and suppose that (a) = 0. Then a.

Use the equation

to establish the following test. Let ƒ have continuous first and second derivatives and suppose that ƒ′(a) = 0. Then

a. ƒ has a local maximum at a if ƒ″ ≤ 0 throughout an interval whose interior contains a;

b. ƒ has a local minimum at a if ƒ″ ≥ 0 throughout an interval whose interior contains a.

f(x) = f(a) + f'(a)(x - a) + f" (c) 2 -(x a)