## Applications of Differentiation: Second Derivative Test

The Second Derivative Test may be used to determine extreme values of a function. Specifically, for critical point c of function f whose second derivative f '' is continuous and f ''(c) = 0:

- For f ''(c) > 0, f (c) is a local minimum,

- For f ''(c) < 0, f (c) is a local maximum,

- For f ''(c) = 0, test is inconclusive

Example:

Find the extreme values and
their locations regarding f
(x) =
2x

^{3}− 3x^{2}using the Second Derivative Test.