Question

What are the relative maximum and minimum of a function?

Answer 1

Maxima and minima:

The values of the functions that represent the maximum and minimum range are referred to as relative maxima and minima or local maximum or local minimum.

The relative maxima and minima are calculated in relation to nearby places. The derivative of the function can be used to calculate it.

The method of finding relative maxima and minima:
The two most common procedures for locating the local maximum and minimum are the first derivative test and the second derivative test.

The input values for which the function returns the maximum and minimum output values are known as relative maxima and minima, respectively.

The function's derivative is extremely useful for locating the function's relative maximum and minimum values.

First-order derivative:

Let $a$ be a critical point for a continuous function $f$.

1. If $f\text{'}\left(x\right)$ changes from positive to negative at $x=a$, then $f\left(a\right)$ is a local maximum.
2. If $f\text{'}\left(x\right)$ changes from negative to positive at $x=a$, then $f\left(a\right)$ is a local minimum.
3. If $f^{\prime }(x)$ does not change sign at $a$, then $f\left(a\right)$ is neither a local maximum or minimum.