Explanation Given: The function is f ( x ) = sin 2 x + 3 on the interval [ − π , π ] . Calculation: Consider the given function is f ( x ) = sin 2 x + 3 on the interval [ − π , π ] . Differentiate the function f ( x ) = sin 2 x + 3 with respect to x . d d x ( f ( x ) ) = d d x ( sin 2 x + 3 ) f ′ ( x ) = d d x ( sin 2 x ) + d d x ( 3 ) = cos 2 x d d x ( 2 x ) + 0 = 2 cos 2 x Set the above derivative to zero, f ′ ( x ) = 0 . 2 cos 2 x = 0 cos 2 x = 0 2 x = cos − 1 ( 0 ) x = 1 2 cos − 1 ( 0 ) On further simplification, x = 1 2 ( ± π 2 + 2 k π ) , k ∈ ℤ x = ± π 4 + k π , k ∈ ℤ Substitute k = 0 , ± 1 , ± 2... in x = ± π 4 + k π , x = − π 4 , π 4 , − 3 π 4 , 3 π 4 , 5 π 4 , − 5 π 4 , ... Thus, the critical points are x = − π 4 , π 4 , − 3 π 4 , 3 π 4 . Substitute x = − π 4 in the function f ( x ) = sin 2 x + 3 , f ( − π 4 ) = sin 2 ( − π 4 ) + 3 = sin ( − π 2 ) + 3 = − 1 + 3 = 2 Thus, f ( − π 4 ) = 2

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ISBN: 9781323178522

Author: Briggs

Publisher: PEARSON

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Chapter 4, Problem 6RE

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To find: The critical points of the function f(x)=sin2x+3 on the given interval and identify the absolute maximum and minimum values and graph the function.

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Chapter 4, Problem 5RE

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Chapter 4 Solutions

CODE/CALC ET 3-HOLE

Ch. 4.1 - Sketch the graph of a function that is continuous...Ch. 4.1 - Sketch the graph of a function that has an...Ch. 4.1 - What is a critical point of a function?Ch. 4.1 - Sketch the graph of a function f that has a local...Ch. 4.1 - Sketch the graph of a function f that has a local...Ch. 4.1 - Absolute maximum/minimum values Use the following...Ch. 4.1 - Absolute maximum/minimum values Use the following...Ch. 4.1 - Absolute maximum/minimum values Use the following...Ch. 4.1 - Absolute maximum/minimum values Use the following...Ch. 4.1 - Local and absolute extreme values Use the...

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The critical points of the function f ( x ) = sin 2 x + 3 on the given interval and identify the absolute maximum and minimum values and graph the function.

Solution Summary: The author explains how to find the critical points of the function f(x)=mathrmsin2x+3 on the given interval and identify the absolute maximum and minimum

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To find: The critical points of the function f(x)=sin2x+3 on the given interval and identify the absolute maximum and minimum values and graph the function.

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