Explanation Given: Function f ( x ) = x + sin x Formula Used: Critical points of the function are the points where the function is defined and its derivative is undefined or zero. Let us assume that p is the critical point of a continuous function f . Moving from left to right If p′ changes from negative to positive at p , then f has local minimum at p If p′ changes from positive to negative at p , then f has local maximum at p Calculation: Function is given as f ( x ) = x + sin x The graph of the above function is as follows:

6th Edition

ISBN: 9781119399353

Author: DA

Publisher: JOHN WILEY+SONS,INC.-CONSIGNMENT

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Chapter 4.1, Problem 19P

To determine

To graph the below function and describe the features of the graph − critical points and if the function is increasing or decreasing. Then explain the shape of graph using derivative

f(x)=x+sinx

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Chapter 4.1, Problem 18P

Chapter 4.1, Problem 20P

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The graph of the function f in the figure below consists of line segments and a quarter of a circle. Let g be the function given by x g(x) = __ f (t)dt. Determine all values of a, if any, where g has a point of inflection on the open interval (-9, 9). 8 y 7 76 LO 5 4 3 2 1 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 ♡. -1 -2 3 -4 56 -5 -6 -7 -8 Graph of f 4 5 16 7 8 9 10

The graph of the function f in the figure below consists of line segments and a semicircle. Let g be the function given by x 9(x) = * f(t)dt. Determine all values of r, if any, where g has a relative minimum on the open interval (-9, 9). y 8 7 6 5 4 32 1 Graph of f x -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9 10 -1 -2 -3 -4 -5 -6 678 -7 -8

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Chapter 4 Solutions

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To graph the below function and describe the features of the graph − critical points and if the function is increasing or decreasing. Then explain the shape of graph using derivative f ( x ) = x + sin x

Solution Summary: The author explains how to graph the function and explain the shape of the graph using derivative f(x)=x+mathrmsin

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To graph the below function and describe the features of the graph − critical points and if the function is increasing or decreasing. Then explain the shape of graph using derivative

f(x)=x+sinx

Want to see the full answer?

Chapter 4 Solutions

To graph the below function and describe the features of the graph − critical points and if the function is increasing or decreasing. Then explain the shape of graph using derivative f ( x ) = x + sin x

Solution Summary: The author explains how to graph the function and explain the shape of the graph using derivative f(x)=x+mathrmsin

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To graph the below function and describe the features of the graph − critical points and if the function is increasing or decreasing. Then explain the shape of graph using derivative f(x)=x+sinx

Want to see the full answer?

Chapter 4 Solutions

To graph the below function and describe the features of the graph − critical points and if the function is increasing or decreasing. Then explain the shape of graph using derivative

f(x)=x+sinx