To find all the local maximum and minimum value of the function and the value of x at which each occur using the graph of the function given.

Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

Solutions

Chapter 2.3, Problem 33E

a.

To determine

To find all the local maximum and minimum value of the function and the value of x at which each occur using the graph of the function given.

Expert Solution

The local maximum and minimum value of the function are 1 and 1,2 respectively and the value of x at which each occur are 3 and 1,2 respectively.

Explanation of Solution

Given information :

The graph of the function is given.

Draw a viewing rectangle on each of the extremum of the graph of the function which is provided in the question.

The graph is shown below:

From the above graph, it can be observed that the point (3,f(3)) is the highest point on the graph of f within the viewing rectangle, so the number f(3)=1 is a local maximum value of the function.

Similarly, it can be observed that the point (2,f(2)) and (1,f(1)) is the lowest points on the graph of f within the viewing rectangle, so the number (2,f(2))=2 and (1,f(1))=1 is the local minimum value of the function.

Hence,

The local maximum and minimum value of the function are 1 and 1,2 respectively and the value of x at which each occur are 3 and 1,2 respectively.

b.

To determine

To find the interval on which the function is increasing and on which the function is decreasing.

Expert Solution

The function f is increasing on [1,3][2,0] and decreasing on (,2][0,1][3,) .

Explanation of Solution

Given information :

The graph of the function is given.

Concept used:

The function is increasing on an interval I if f(x1)<f(x2) whenever x1<x2 in I .

The function is decreasing on an interval I if f(x1)>f(x2) whenever x1<x2 in I .

The graph of the function is shown below:

Use definition of increasing and decreasing function.

From the above graph, it can be observed that the function f is increasing on [1,3][2,0] as f(1)=1<f(3)=1 for 1<1 and f(2)=2<f(0)=0 for 2<0 respectively and decreasing on (,2][0,1][3,) as f()=>f(2)=2 for 2< , f(0)=0>f(1)=1 for 0<1 and f(3)=1>f()= for 3< respectively.

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