notes/education/math/MATH1210 (calc 1)/Max and Min.md

Absolute Maximum/Minimum

A function f has an absolute maximum at c if f(c) >= f(x). We call f(c) the maximum value of f. The absolute maximum is the largest possible output value for a function.

A function f has an absolute minimum at c if f(c) <= f(x). f(c) is the absolute minimum value of f. The absolute minimum is the smallest possible output value for a function.

• Where the derivative of a function is zero, there is either a peak or a trough.

Critical Numbers

A number is considered critical if the output of a function exists and \dfrac{d}{dx} is zero or undefined.