Precalculus with Limits: A Graphing Approach
Precalculus with Limits: A Graphing Approach
7th Edition
ISBN: 9781305071711
Author: Ron Larson
Publisher: Brooks/Cole
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Chapter 5.3, Problem 92E

a.

To determine

To graph: The given function in the given interval and approximate maximum and minimum points (to four decimal places) of the graph.

a.

Expert Solution
Check Mark

Answer to Problem 92E

The approximate maximum and minimum points are:

Maxima: (0,1),(3.1416,1),(6.2832,1)

Minima: (1.5708,−1),(4.7124,−1)

Explanation of Solution

Given information:

The following function:

  f(x)=cos2x

The following interval:

  [0,2π)

Graph:

Sketch the graph using graphing utility.

Step 1: Press WINDOW button to access the Window editor.

Step 2: Press Y= button.

Step 3: Enter the expression cos2x which is required to graph.

Step 4: Press GRAPH button to graph the function.

The graph is obtained as:

  Precalculus with Limits: A Graphing Approach, Chapter 5.3, Problem 92E

Interpretation:

Using TRACE feature on the calculator, the maximum and minimum points are obtained as:

Maxima: (0,1),(3.1416,1),(6.2832,1)

Minima: (1.5708,−1),(4.7124,−1)

b.

To determine

To solve: The given trigonometric equation using calculus and verify that the x-coordinates of the maximum and minimum points of f are among its solutions.

b.

Expert Solution
Check Mark

Answer to Problem 92E

The solution of the trigonometric equation is:

  x=nπ2

Explanation of Solution

Given information:

The following equation:

  −2sin2x=0

Calculation:

The given equation is solved as:

  −2sin2x=0        [Given]sin2x=0             [Divide both sides by −2]2x=0+nπ          [Using inverse trigonometric function]x=nπ2                 [Divide both sides by 2]

On substituting the x-coordinates of the maximum and minimum points of f , the following solutions are obtained:

  −2sin2x=−2sin(2×0)=−2sin0=0−2sin2x=−2sin(2×3.1416)=−2sin(6.2832)=0−2sin2x=−2sin(2×6.2832)=−2sin(12.5664)=0−2sin2x=−2sin(2×1.5708)=−2sin(12.5664)=0−2sin2x=−2sin(2×4.7124)=−2sin(9.4248)=0

Since every answer corresponds to 0 , the x-coordinates of the maximum and minimum points of fare among the solutions.

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Chapter 5.3, Problem 91E
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Chapter 5.3, Problem 93E

Chapter 5 Solutions

Precalculus with Limits: A Graphing Approach

Ch. 5.1 - Prob. 1ECh. 5.1 - Prob. 2ECh. 5.1 - Prob. 3ECh. 5.1 - Prob. 4ECh. 5.1 - Prob. 5ECh. 5.1 - Prob. 6ECh. 5.1 - Prob. 7ECh. 5.1 - Prob. 8ECh. 5.1 - Prob. 9ECh. 5.1 - Prob. 10E
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