help [(critical points -extrema]

Question

Answer 1

(7)

Step 1:

Definition of local maximum and local minimum :

1. The number c is a local maximum value of f if when is near c.

2.The number c is a local minimum value of  f if when is near c.

Definition of absolute maximum and absolute minimum :

Let c be a number in the domain of a function f.

1.The number c is a absolute maximum value of f on if for all in .

2.The number c is a absolute minimum value of f on if for all in .

Step 2:

The function is and the interval is .

Graph :

Graph the function in the interval .

Observe the graph.

The graph of the function decreases as the values of increases.

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 .

Answer 2

(8)

Step 1:

Definition of local maximum and local minimum :

1. The number c is a local maximum value of f if when is near c.

2.The number c is a local minimum value of  f if when is near c.

Definition of absolute maximum and absolute minimum :

Let c be a number in the domain D of a function f.

1.The number c is a absolute maximum value of f on D if for all in D.

2.The number c is a absolute minimum value of f on D if for all in D.

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 .

Answer 3

(9)

Step 1:

Definition of local maximum and local minimum :

1. The number c is a local maximum value of f if when is near c.

2.The number c is a local minimum value of  f if when is near c.

Definition of absolute maximum and absolute minimum :

Let c be a number in the domain D of a function f.

1.The number c is a absolute maximum value of f on D if for all in D.

2.The number c is a absolute minimum value of f on D if for all in D.

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 .