Explanation Given: The function is f ( x ) = 2 cos ( 3 x ) + 3 cos ( 2 x ) . Concept used: Critical points: For a function f ( x ) the critical points exists at such points such that the value of f ′ ( x ) is 0 or the f ′ ( x ) does not exists. Calculation: The given function is expressed as follows: f ( x ) = 2 cos ( 3 x ) + 3 cos ( 2 x ) …..(1) Differentiate equation (1) as shown below: f ′ ( x ) = d ( 2 cos ( 3 x ) ) d x + d ( 3 cos ( 2 x ) ) d x = − 6 sin ( 3 x ) − 6 sin ( 2 x ) To obtain the critical points for the given function solve the equation f ′ ( x ) = 0 as shown below: f ′ ( x ) = 0 − 6 sin ( 3 x ) − 6 sin ( 2 x ) = 0 sin ( 3 x ) + sin ( 2 x ) = 0 2 sin ( 3 x + 2 x 2 ) cos ( 3 x − 2 x 2 ) = 0 Further solve the above equation. 2 sin ( 3 x + 2 x 2 ) cos ( 3 x − 2 x 2 ) = 0 sin ( 5 x 2 ) cos ( x 2 ) = 0 Use the zero product property to solve the above equation. First solve the equation sin ( 5 x 2 ) = 0 as shown below: sin ( 5 x 2 ) = 0 sin ( 5 x 2 ) = sin ( n π ) 5 x 2 = n π x = 2 n π 5 The value of x is expressed as shown below: x = 2 n π 5 ….(2) In the above equation n = 0 , 1 , 2 , 3... . Now, solve the equation cos ( x 2 ) = 0 as shown below: cos ( x 2 ) = 0 cos ( x 2 ) = cos ( ( 2 n + 1 ) π 2 ) x 2 = ( 2 n + 1 ) π 2 x = ( 2 n + 1 ) π The value of x is expressed as shown below: x = ( 2 n + 1 ) π …

4th Edition

ISBN: 9781319545956

Author: Rogawski

Publisher: MAC HIGHER

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Question

Chapter 4.2, Problem 64E

To determine

To find:

The critical points of the function f(x)=2cos(3x)+3cos(2x) in the interval [0,2π] and check the answer with the graph of the function f(x).

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Chapter 4.2, Problem 63E

Chapter 4.2, Problem 65E

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Chapter 4 Solutions

CALCULUS W/ACHIEVE PLATFORM

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Prob. 63CRE Ch. 4 - Prob. 64CRE Ch. 4 - Prob. 65CRE Ch. 4 - Prob. 66CRE Ch. 4 - Prob. 67CRE Ch. 4 - Prob. 68CRE Ch. 4 - Prob. 69CRE Ch. 4 - Prob. 70CRE Ch. 4 - Prob. 71CRE Ch. 4 - Prob. 72CRE Ch. 4 - Prob. 73CRE Ch. 4 - Prob. 74CRE Ch. 4 - Prob. 75CRE Ch. 4 - Prob. 76CRE Ch. 4 - Prob. 77CRE Ch. 4 - Prob. 78CRE Ch. 4 - Prob. 79CRE Ch. 4 - Prob. 80CRE Ch. 4 - Prob. 81CRE Ch. 4 - Prob. 82CRE Ch. 4 - Prob. 83CRE Ch. 4 - Prob. 84CRE Ch. 4 - Prob. 85CRE Ch. 4 - Prob. 86CRE Ch. 4 - Prob. 87CRE Ch. 4 - Prob. 88CRE Ch. 4 - Prob. 89CRE

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The critical points of the function f ( x ) = 2 cos ( 3 x ) + 3 cos ( 2 x ) in the interval [ 0 , 2 π ] and check the answer with the graph of the function f ( x ) .

Solution Summary: The author analyzes the critical points of a function f(x).

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To find:

The critical points of the function f(x)=2cos(3x)+3cos(2x) in the interval [0,2π] and check the answer with the graph of the function f(x).

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Chapter 4 Solutions

The critical points of the function f ( x ) = 2 cos ( 3 x ) + 3 cos ( 2 x ) in the interval [ 0 , 2 π ] and check the answer with the graph of the function f ( x ) .

Solution Summary: The author analyzes the critical points of a function f(x).

Concept explainers

Videos

To find: The critical points of the function f(x)=2cos(3x)+3cos(2x) in the interval [0,2π] and check the answer with the graph of the function f(x).

Want to see the full answer?

Chapter 4 Solutions

To find:

The critical points of the function f(x)=2cos(3x)+3cos(2x) in the interval [0,2π] and check the answer with the graph of the function f(x).