Step 1:

(a)

Definition of local maximum and local minimum :

1. The number $\"\"$ is a local maximum value of $\"\"$ if $\"\"$ when $\"\"$ is near $\"\"$ .

2.The number $\"\"$ is a local minimum value of $\"\"$ if $\"\"$ when $\"\"$ is near $\"\"$ .

Definition of absolute maximum and absolute minimum :

Let $\"\"$ be a number in the domain $\"\"$ of a function $\"\"$ .

1.The number $\"\"$ is a absolute maximum value of $\"\"$ on $\"\"$ if $\"\"$ for all $\"\"$ in $\"\"$ .

2.The number $\"\"$ is a absolute minimum value of $\"\"$ on $\"\"$ if $\"\"$ for all $\"\"$ in $\"\"$ .

Step 2:

The function is $\"\"$ in the $\"\"$ . \ \

Graph :

Graph the function $\"\"$ in the interval $\"\"$ .

$\"\"$

Observe the graph.

The graph of the function $\"\"$ is decreasing as the values of $\"\"$ .

Hence the function has no global extrema and no local extrema.

Solution:

The function has no global extrema and no local extrema in the interval $\"\"$ .

(b)

Step 1:

Definition of local maximum and local minimum :

1. The number $\"\"$ is a local maximum value of $\"\"$ if $\"\"$ when $\"\"$ is near $\"\"$ .

2.The number $\"\"$ is a local minimum value of $\"\"$ if $\"\"$ when $\"\"$ is near $\"\"$ .

Definition of absolute maximum and absolute minimum :

Let $\"\"$ be a number in the domain $\"\"$ of a function $\"\"$ .

1.The number $\"\"$ is a absolute maximum value of $\"\"$ on $\"\"$ if $\"\"$ for all $\"\"$ in $\"\"$ .

2.The number $\"\"$ is a absolute minimum value of $\"\"$ on $\"\"$ if $\"\"$ for all $\"\"$ in $\"\"$ .

Step 2:

The function is $\"\"$ in the $\"\"$ . \ \

Graph :

Graph the function $\"\"$ in the interval $\"\"$ .

$\"\"$

Observe the graph.

$\"\"$ on its domain $\"\"$ .

Absolute maximum is $\"\"$ .

$\"\"$ on its domain $\"\"$ .

Absolute minimum is $\"\"$ .

Solution:

Absolute maximum is $\"\"$ .

Absolute minimum is $\"\"$ .

(c)

Step 1:

Definition of local maximum and local minimum :

1. The number $\"\"$ is a local maximum value of $\"\"$ if $\"\"$ when $\"\"$ is near $\"\"$ .

2.The number $\"\"$ is a local minimum value of $\"\"$ if $\"\"$ when $\"\"$ is near $\"\"$ .

Definition of absolute maximum and absolute minimum :

Let $\"\"$ be a number in the domain $\"\"$ of a function $\"\"$ .

1.The number $\"\"$ is a absolute maximum value of $\"\"$ on $\"\"$ if $\"\"$ for all $\"\"$ in $\"\"$ .

2.The number $\"\"$ is a absolute minimum value of $\"\"$ on $\"\"$ if $\"\"$ for all $\"\"$ in $\"\"$ .

Step 2:

The function is $\"\"$ in the $\"\"$ . \ \

Graph :

Graph the function $\"\"$ in the interval $\"\"$ .

$\"\"$

Observe the graph.

There is no absolute maximum, because the highest part of the graph is leads to a hole.

$\"\"$ on its domain $\"\"$ .

Absolute minimum is $\"\"$ .

Solution: \ \

Absolute minimum is $\"\"$ .