Chapter 4.3, Problem 49E

a.

To determine

To find the absolute maximum and absolute minimum.

Answer to Problem 49E

The absolute maximum is $(1,2)$ and the absolute minimum at $(3,-2)$ .

Explanation of Solution

Given:

$x$	0	1	2	3
$f$	0	2	0	-2
$f\text{'}$	3	0	Does not exist	-3
$f\text{'}\text{'}$	0	-1	Does not exist	0

$x$	0<x<1	1<x<2	2<x<3
$f$	+	+	-
$f\text{'}$	+	-	-
$f\text{'}\text{'}$	-	-	-

Calculation:

The absolute maximum is where the $f\text{'}\text{'}$ decreasing and $f\text{'}\text{'}$ increasing.

From the given information,

The absolute maximum is $(1,2)$ and the absolute minimum at $(3,-2)$

.

b.

To determine

To find the point of inflection .

Answer to Problem 49E

There is no point of inflection.

Explanation of Solution

Given:

$x$	0	1	2	3
$f$	0	2	0	-2
$f\text{'}$	3	0	Does not exist	-3
$f\text{'}\text{'}$	0	-1	Does not exist	0

$x$	0<x<1	1<x<2	2<x<3
$f$	+	+	-
$f\text{'}$	+	-	-
$f\text{'}\text{'}$	-	-	-

Calculation:

The point of inflection is the point where $f\text{'}=0$ .

From the given information,

There is no point of inflection.

c.

To determine

The find the graph

Answer to Problem 49E

The graph is

  

Explanation of Solution

Given:

$x$	0	1	2	3
$f$	0	2	0	-2
$f\text{'}$	3	0	Does not exist	-3
$f\text{'}\text{'}$	0	-1	Does not exist	0

$x$	0<x<1	1<x<2	2<x<3
$f$	+	+	-
$f\text{'}$	+	-	-
$f\text{'}\text{'}$	-	-	-

Calculation:

From the graph is

The end points are $(0,0)$ , $(3,0)$ ,

There is no straight line in the graph.

The resulting graph will be