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 formula for the derivative of a function $f$ is given. How many critical numbers does $f$ have?

$ f'(x) = 5e^{-0.1 |x|} \sin x - 1 $

Video Answer

Solved by verified expert

This problem has been solved!

Try Numerade free for 7 days

Like

Report

Official textbook answer

Video by Yuki Hotta

Numerade Educator

This textbook answer is only visible when subscribed! Please subscribe to view the answer

01:43

Wen Zheng

00:12

Amrita Bhasin

Calculus 1 / AB

Calculus 2 / BC

Chapter 4

Applications of Differentiation

Section 1

Maximum and Minimum Values

Derivatives

Differentiation

Volume

Oregon State University

University of Michigan - Ann Arbor

University of Nottingham

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.

02:10

A formula for the derivati…

12:10

04:07

01:03

Find all critical numbers …

01:12

01:16

Find the critical numbers …

01:15

02:15

Okay, let's go ahead and answer this question. So the question tells you why close to five e to the native 50.1 absolutely affects time. Sign of X minus one. Um, how many critical points do we have when this Why is actually a derivative of a function f Okay, so to find a critical point, what's important to remember is that, first of all, it has to be a value of zero. And second of all, it has to actually be a sign change. So F prime has to be zero in the points around. It has to be from negative to positive or positive to negative. If you take a look at the graph, you can see that it's not one of those, um, shapes where it's on Lee touching the X axis. So it's very likely that it's not going to be a point where if prime is equal to zero yet, it's not a critical point. So we're not gonna have to worry about those things now. It's very important to see that there is a negative one right there, because if it's not, you can clearly see that, um, it zero is the average value off this function, and it'll very likely have infinitely many points as a critical. However, the negative one shifts it downwards. So we have to be very careful with how many zeros this thing has. Okay, because let's do something really interesting right now. Five need to the Maybe there's 0.1. Absolute value of X shifted one ground, as you can see. Oh, let me try to change it. There you go. This is the number that is multiplied in front of the sine X. So it behaves like it amplitude. So how much up and down it goes? Depends on the value of this guy, Okay? And it basically traces on top of the highest point where this Greiff graph can go. And as you can see, the further you go towards the right side, it gets closer and closer to zero. So it seems like at a certain X input, the height is not going to be tall enough that it can touch the X axis even though the graph wants to get close to it anymore. Okay, That's one of the interesting things that you could see. Now we're going to count how many points it actually crosses through. Um, why equals to zero. So we're going to start here. You gotta be very, very careful here. If you go far enough, it looks like it actually touches the X axis. But if you get closer, you can see that it actually is not. So this point, even though it's close, it actually doesn't count as a, um zero. So let's count. 12 34 56 789 10 and Tenet ISS So you can see that all of the's 10 points are ex intercepts, and it goes from negative positive to negative here, negative to positive there. So it's a sign change. So, indeed, all of these zeros represents a critical point off F because F Prime is equal to zero at those points. So to answer the question, how many critical critical points should f have? Well, it's going to be 10, and that's I answer this question

View More Answers From This Book

Find Another Textbook

07:00

A formula for calculating the magnitude of an earthquake is M = Hlo…

01:44

Without using calculator; compute the sine and cosine of 150 by using the re…

02:37

What are the values of the sixtrignometric functions for the triangle be…

07:48

20. The median home value ins Indiana and Alabama (adjusted for inf…

02:12

The graph above is a transformation of thefunction x2x2Write an equa…

02:40

Starting with the graph of m(x) = 2*, determine the formula that re…

01:38

Write an equation for thefunction graphed below

Write an equatio…

01:09

The area A(t) of a circular shape is growing at constant rate. If the area i…

01:19

Based on the graph above; determine the Use f(z) as the outpu…

02:45

Which of the following can be approximated to binomial?type of payment i…