Here we’ll practice using the first derivative test.

The function has two critical points. If we call these critical point and , and order them such that , then

On , is

On , is

On , is

Consider restricted to the domain .

On this interval, the absolute maximum value of is .

On this interval, the absolute minimum value of is .

Consider the function .

What is the domain of this function?

Domain:

has only one critical point. Call this critical point .

On , is

On , is

On , is

is an absolute

The function has two critical points and one point where is undefined. If we call these points , , and and order them such that , then

On , is

On , is

On , is

On , is

is the location of a

is the location of a

is the location of a

If then the function has two critical points and one point where the function is undefined. If we call these points , , and and order them such that , then

On , is

On , is

On , is

On , is

is the location of a

is the location of a

is the location of a

The function has two critical points. If we call these critical points and , and order them such that , then

On , is

On , is

On , is

is the location of a

is the location of a