help?(critical points -extrema]

Question

Answer 1

Step 1:

A critical number of a function is a number in the domain of such that either or does not exist.

is used to determine whether the function is increasing or decreasing.

Hence critical points are the points where the function changes its state from increasing to decreasing or vice versa.

Functions can have "hills and valleys" places where they reach a critical point.

Observe the graph.

The graph of the from changes its state at and .

Hence the critical numbers are and .

Solution:

The critical numbers are and .