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 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

Answer to Problem 33E

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.

  Precalculus: Mathematics for Calculus - 6th Edition, Chapter 2.3, Problem 33E , 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 33E , additional homework tip  2

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

Answer to Problem 33E

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.

  Precalculus: Mathematics for Calculus - 6th Edition, Chapter 2.3, Problem 33E , 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 33E , additional homework tip  4

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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