BuyFind

Precalculus: Mathematics for Calcu...

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

Precalculus: Mathematics for Calcu...

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

Solutions

Chapter 2.3, Problem 34E

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

Answer to Problem 34E

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

Explanation of Solution

Given information :

The graph of the function is given.

  Precalculus: Mathematics for Calculus - 6th Edition, Chapter 2.3, Problem 34E , additional homework tip  1

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:

  Precalculus: Mathematics for Calculus - 6th Edition, Chapter 2.3, Problem 34E , additional homework tip  2

From the above graph, it can be observed that the point (2,f(2)) and (1,f(1)) are the highest point on the graph of f within the viewing rectangle, so the number (2,f(2))=3 and (1,f(1))=2 is a local maximum value of the function.

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

Hence,

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

b.

To determine

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

Expert Solution

Answer to Problem 34E

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

Explanation of Solution

Given information :

The graph of the function is given.

  Precalculus: Mathematics for Calculus - 6th Edition, Chapter 2.3, Problem 34E , additional homework tip  3

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:

  Precalculus: Mathematics for Calculus - 6th Edition, Chapter 2.3, Problem 34E , additional homework tip  4

Use definition of increasing and decreasing function.

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

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