Download the App!
Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.
Question
Answered step-by-step
(a) Find the intervals of increase or decrease.(b) Find the local maximum and minimum values.(c) Find the intervals of concavity and the inflection points.(d) Use the information from parts $ (a) - (c) $ to sketch the graph. Check your work with a graphing device if you have one.
$ S(x) = x - \sin x $, $ 0 \leqslant x \leqslant 4\pi $
Video Answer
Solved by verified expert
This problem has been solved!
Try Numerade free for 7 days
Like
Report
Official textbook answer
Video by Wen Zheng
Numerade Educator
This textbook answer is only visible when subscribed! Please subscribe to view the answer
Calculus 1 / AB
Calculus 2 / BC
Chapter 4
Applications of Differentiation
Section 3
How Derivatives Affect the Shape of a Graph
Derivatives
Differentiation
Volume
University of Michigan - Ann Arbor
Idaho State University
Boston College
Lectures
04:35
In mathematics, the volume of a solid object is the amount of three-dimensional space enclosed by the boundaries of the object. The volume of a solid of revolution (such as a sphere or cylinder) is calculated by multiplying the area of the base by the height of the solid.
06:14
A review is a form of evaluation, analysis, and judgment of a body of work, such as a book, movie, album, play, software application, video game, or scientific research. Reviews may be used to assess the value of a resource, or to provide a summary of the content of the resource, or to judge the importance of the resource.
03:12
(a) Find the intervals of …
0:00
(a) Find the intervals…
05:23
04:15
02:43
06:33
04:31
01:08
Part, i find the intervals of increase or decrease part. So f s, prime, is equal to 1 minus cosine x, which is always greater than 0. So behalf has interval from 0 to 4 pi, so f s prim is greater than 0. So, as is increasing part b so from the result in part, a the function as x has no local maximum and minimum values. Part c find the intervals of concavity and the inflection points light as from so this is equal to sine x. Let the second derivative be equal to 0, with half x is equal to 0 pi 2 pi 3 pi 4 pi and the interval from 0 to pi. Second derivative is positive, so the function is so f s x, concaves interval from pit to pi. So as propriis negative, so as is a concave tom and 2 pi to 3 pi, half second derivative is positive, so its function is concave r, 3 pi to 4 pi as proprium is negative, was function is conciptinflection. Points are pi 2 pi, 3 pi part d. Use the information from parts a to c to sketch the graph, so we can sketch the graph as follows: 0 pi, 2 pi, 3 pi, 4 pilik and by using the graphing device we can graph is a function as follows. So this is the graph of the function x, minus sine x,
View More Answers From This Book
Find Another Textbook
04:55
Ok, so im brand new at trigonometry. If i have a right triangle with an acu…
What is a possible career can I pursue
01:15
In a certian lottery, 4 differnt numbers between 1 and 11 inclusive are draw…
00:43
How do I Factor the expression a y - a^{6} y^{6} ?
01:24
A district mathematics test for all third graders had a normal distribution …
02:26
1. Two roommates, roommate A and roommate B, are about to go cruising with a…
01:52
a farmer has a triangular garden with two sides at right angles and the thir…
03:05
In the Federal Trade Commission (FTC) Price Check" study of electronic …
03:24
a flagpole 25 feet tall stands on a top of a building. from a point in the s…
01:26
The maximum temperature on Thursday was 18 degree celsius.On Friday it incre…