help?---[(critical points -extrema]

Question

Answer 1

(6)

Step 1:

Definition of local extreme :

Functions can have "hills and valleys" places where they reach a minimum or maximum value.

Definition of absolute extreme :

The maximum or minimum over the entire function is called an "Absolute" or "Global" maximum or minimum.

There is only one global maximum (and one global minimum) but there can be more than one local maximum or minimum.

Observe the graph :

is a absolute minimum as well as local minimum.

is a absolute minimum as well as local minimum.

is a absolute maximum as well as local maximum.

is a absolute maximum as well as local maximum.

is a local minimum.

Solution :

The absolute maximum are and .

The absolute minimum are and .

The local maximum are and .

The local minimum are , and .