• ### Critical Point

A number x in the domain of a function f such that f'(x) = 0.

• ### Global Maximum

A value f (x0) that is greater than or equal to any other value f (x) that f takes on over its domain.

• ### Global Minimum

A value f (x0) that is less than or equal to any other value f (x) that f takes on over its domain.

• ### Inflection Point

A number x in the domain of a function f such that f’’(x) = 0.

• ### Local Maximum

A value f (x0) that is greater than or equal to any other value f (x) for x in some interval about x0.

• ### Local Minimum

A value f (x0) that is less than or equal to any other value f (x) for x in some interval about x0.

• ### First Derivative Test

A critical point x0 of a function f is a local maximum if the first derivative f' changes sign from positive to negative at x0. Correspondingly, x0 is a local minimum is f' changes sign from negative to positive there.

• ### Second Derivative Test

A critical point x0 of a function f is a local maximum if the second derivative f''(x0) is negative. It is a local minimum if f''(x0) is positive. (It is also possible that f''(x0) = 0, in which case the critical point is also an inflection point.)

• ### Concave Up

A function f (x) is concave up at x0 if f''(x0) > 0.

• ### Concave Down

A function f (x) is concave down at x0 if f''(x0) < 0.