Download the App!

Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.

Use the guidelines of this section to sketch the curve.

$ y = (1 - x)e^x $

Get the answer to your homework problem.

Try Numerade free for 7 days

Like

Report

Because of the change in concavity the inflection point is:$(-1, f(-1))=\left(-1, \frac{2}{e}\right) \approx(-1,0.736)$

Calculus 1 / AB

Calculus 2 / BC

Chapter 4

Applications of Differentiation

Section 5

Summary of Curve Sketching

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.

0:00

Use the guidelines of this…

01:39

13:27

01:13

03:27

08:38

domain for this function is X is all real. The intercepts are 01 and 10 There is no symmetry. And for Assam, toots, um, there's no vertical, but we can test for horizontal. There is one at, um negative infinity. So let's let's test as X approaches negative infinity for a function one minus x to the, um times e to the X. And this limit will give us because it's negative Infinity, It's going to give us zero. So as X approaches negative infinity or why value is going to approach zero. All right, so that is our esteemed too. And now we can look for increasing and decreasing intervals. So why prime? Why? Prime is equal to negative x you to the ex. And if we set our first derivative to zero, we can see that a critical 00.0. So if we do the first derivative test around zero of print, so it's positive and this interval negative and this interval, So that means that zero is going from increasing to decreasing. So at zero, we have a local max and you know that 01 is our point. So 01 is our local necks. So that's it for the first derivative test. And now we can take the second derivative and find the cone cavity of her graph. So why Double prime is equal to negative X minus one times E to the power of X. And if we set that equal to zero, we see a critical point at negative one. So the second derivative test for Con Cavity around negative one. We can see it's pot. It's Kong cave up here and it's Kong cave down here so can't give up and con cave down. And if we test where f of negative one is, we see that it's 0.7 positive 0.7, all right, And also because this is changing from positive to negative. There's a sign change so that this is an inflection point. Okay, so that's it for the second derivative test, and now we can graft. So we haven't asked himto. Let's grab that first in green. We haven't asked him to at like, Well, zero and we have a new intercept at 01 So it's say this is one. All right, this is one and say this is negative one. All right, So now we have an intercept at 01 and 10 and we know that our graph as approaches negative infinity. So in this direction, it's going to go to zero the line zero. So the more is over here, it's gonna approach zero. But let's see what's going on here. So since this is a max, it's going to be increasing before zero. But after zero, it's gonna decrease. All right, so it's gonna decrease here after zero, and it's gonna be calling cave down. Gonna hit the access and become came down. And then on the other side, it's going to be con cave up. Um, after it hits the inflection point. So about negative 10.7. So let's say that's about here. This is our inflection point. So it's gonna be con cave up and increasing and then con cave now in here. This is a graph

View More Answers From This Book

Find Another Textbook

Numerade Educator

02:03

During weekends, your family loves to have Pizza Party. Your mother will ma…

02:14

A 20-floor tall building makes an angle of elevation of P degree from a poin…

01:22

A gardener planted a tree 0.65 m long the tree increases in height by 0.03 m…

00:41

A hiker bought a rope of length 32,975cm. He cut it into 25 equalpieces.…

01:58

A CENTRAL ANGLE OF 45 DEGREES SUBTENDS AN ARC OF 12 CM. WHAT IS THE RADIUS O…

02:07

A girl observed that the average of 20 numbers is 35 when she writes a numbe…

01:15

Subtract 3m^2 -4n - 2 from- 6m^2+ 8 -24

02:11

A certain sum of money is divided into three parts in the ratio 5 : 7 :8. If…

02:02

A conical container is fully filled with petrol .the radius is 10 m and the …

01:50

A man saves 10 % of his monthly income. After a year, he finds that he has 1…