Explanation Definition used: The function is decreasing if f ′ ( x ) < 0 and function increasing if f ′ ( x ) > 0 . Calculation: The function is given by f ( x ) = x − sin x . Find the derivative of f ( x ) = x − sin x as follows. f ′ ( x ) = d d x ( x − sin x ) = 1 − cos x Setting f ′ ( x ) = 0 and obtain the critical point as follows. 1 − cos x = 0 cos x = 1 x = 2 n π , n = 0 , 1 , 2 , ⋯ Here, the critical point is x = 2 n π , n = 0 , 1, 2, … . Now choose minimum interval and discuss the nature of f ( x ) as follows. Choose n = 1, 2, 3 , so the interval notation ( − ∞ , 2 π ) , ( 2 π , 4 π ) , ( 4 π , 6 π ) and ( 6 π , ∞ ) . Determine the nature of f ( x ) as follows. Intervals f ′ ( x ) = 1 − cos x f ( x ) − ∞ < x < 2 π f ′ ( 0 ) = 1 − cos ( 0 ) = 1 − 1 f ′

Applied Calculus for the Managerial, Life, and Social Sciences

10th Edition

ISBN: 9781305887831

Author: Tan

Publisher: CENGAGE CO

See similar textbooks

Concept explainers

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as:

Videos

Question

Chapter 12.3, Problem 70E

To determine

Whether the statement “The graph of f(x)=x−sinx is non-decreasing on (−∞,∞)” is true or false. If it is true, explain why it is true. If it is false, give an example to show why it is false.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 12.3, Problem 69E

Chapter 12.3, Problem 71E

Students have asked these similar questions

T 1 7. Fill in the blanks to write the calculus problem that would result in the following integral (do not evaluate the interval). Draw a graph representing the problem. So π/2 2 2πxcosx dx Find the volume of the solid obtained when the region under the curve on the interval is rotated about the axis.

38,189 5. Draw a detailed graph to and set up, but do not evaluate, an integral for the volume of the solid obtained by rotating the region bounded by the curve: y = cos²x_for_ |x| ≤ and the curve y y = about the line x = =플 2 80 F3 a FEB 9 2 7 0 MacBook Air 3 2 stv DG

Find f(x) and g(x) such that h(x) = (fog)(x) and g(x) = 3 - 5x. h(x) = (3 –5x)3 – 7(3 −5x)2 + 3(3 −5x) – 1 - - - f(x) = ☐

Chapter 12 Solutions

Applied Calculus for the Managerial, Life, and Social Sciences

Ch. 12.1 - Prob. 1CQ Ch. 12.1 - Prob. 2CQ Ch. 12.1 - Prob. 3CQ Ch. 12.1 - In Exercises 14, express the angle shown in the...Ch. 12.1 - Prob. 2E Ch. 12.1 - Prob. 3E Ch. 12.1 - Prob. 4E Ch. 12.1 - Prob. 5E Ch. 12.1 - Prob. 6E Ch. 12.1 - Prob. 7E

Knowledge Booster

$Calculus$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

Whether the statement “The graph of f ( x ) = x − sin x is non-decreasing on ( − ∞ , ∞ ) ” is true or false. If it is true, explain why it is true. If it is false, give an example to show why it is false.

Solution Summary: The author explains whether the statement "The graph of f(x)=x-mathrmsinx" is true or false.

Concept explainers

Videos

Whether the statement “The graph of f(x)=x−sinx is non-decreasing on (−∞,∞)” is true or false. If it is true, explain why it is true. If it is false, give an example to show why it is false.

Want to see the full answer?

Chapter 12 Solutions