How do you determine the absolute maximum and minimum values of a continuous function on a closed interval?

Steps are detailed below.

Step-by-step explanation:

The steps to determine the absolute maximum and minimum values of a continuous function on a closed interval are;

For example, if we have a function f(x) = x³ - 3x + 2 on the interval (-3, 4)

The steps are;

Step 1:

We will find the first derivative of f(x) which is; f'(x) = 3x² - 3.

Then we will find the critical values of this derivative. The critical values are the values of x that makes f'(x) = 0. But these critical values must fall in between the given interval (-3, 4)

Step 2:

Plug in the critical values gotten in step 1 above into the original f(x) function and note down the answers.

Step 3;

Plug in the endpoint values on the interval (-3, 4) given in the question into the original f(x) function and note down the answers.

Step 4;

The highest and lowest values of f(x) gotten in steps 2 & 3 are the absolute maximum and absolute minimum values respectively of the continuous function f(x).

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step-by-step explanation: