Download the App!

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

Make a careful sketch of the graph of $ f $ and below it sketch the graph of $ f' $ in the same manner as in Exercises 4-11. Can you guess a formula for $ f'(x) $ from its graph?

$ f(x) = e^x $

Get the answer to your homework problem.

Try Numerade free for 7 days

Like

Report

The slope at 0 appcars to be 1 and the slope at 1 appears 0. Since to be 2.7 . As $x$ decreases, the slope gets closer to the graphs are so similar, we might gacss that $f^{\prime}(x)=e^{x}$.

Calculus 1 / AB

Chapter 2

Limits and Derivatives

Section 8

The Derivative as a Function

Limits

Derivatives

Missouri State University

University of Michigan - Ann Arbor

Boston College

Lectures

04:40

In mathematics, the limit of a function is the value that the function gets very close to as the input approaches some value. Thus, it is referred to as the function value or output value.

In mathematics, a derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a moving object with respect to time is the object's velocity. The concept of a derivative developed as a way to measure the steepness of a curve; the concept was ultimately generalized and now "derivative" is often used to refer to the relationship between two variables, independent and dependent, and to various related notions, such as the differential.

01:46

Make a careful sketch of t…

03:07

01:37

01:12

0:00

03:12

01:34

00:58

$16-18$ Make a careful ske…

01:18

02:09

this problem for seventeen of the Stuart Calculus eighth edition, Section two point eight make a careful sketch of the graph of F and blew it sketch the graph of every time in the same manner as an exercise is for true love. Can you guess a formula for halftime from its crap? So first, let's plot after of X equals e to the X and the top craft were were sketching Ah, good. The graph of F and looks roughly like this One of the key points is this point zero one, not a word that is the white intercept of the function. Because at X equals zero, it is there is one. Ah, and we see that the limit is expertise needed Infinity a zero and that limit is exported infinities infinity. So this increases. Ah, as a X goes towards infinity. Now I may be a bit difficult, but we're going to attempt to drop the graph of time by using the slopes of the tangent lines that our attention to this function f the easy are one of the easier ones to look at is as X approaches negative infinity. We see that dysfunction that pulls out. Search them. The slopes of the tension line decrease in Stevenage and in value until it becomes almost flat. A sex person. Negative infinity. So we're going to get this Ah, decrease of the slope towards zero. Because the slopes of the tension lines approach zero. As we approach any other affinity arm, we can estimate the slope of the tangent line at X equals zero here and where we end up. If we were to fear that's not exactly the slope of the tension line at X equals zero ends up being exactly one. So there's an interesting result. And what is more interesting is that if we continue to find the slopes of each of the tendon lines as X increases, we will begin. We will continue to plot what is exactly the same graph as F arms. So in reality, what we have just plotted is the functioning of the ex. And this is consistent with our definition for this function, any of the ex because we know that the definition of either the ex is indeed itself even the X and so they're dirt of craft is exactly the same esteem original graph, and it at every point is the slope of the tangent line to dysfunction at every point

View More Answers From This Book

Find Another Textbook

Numerade Educator

01:06

If all 2,a,6 is in AP then the value of a is

00:30

find the cost of fencing a rectangular field 80 m long and 35 m wide at a ra…

01:22

if alpha and beta are the zeros and the quadratic polynomial FX = x square m…

05:07

If a loan of Rs. 30,000 is to be paid in 5 annual installments with interest…

02:13

Total sales RS. 3,00,000, Debtors at the beginning RS.25,000 and closing Deb…

05:14

In a survey of 195 people it was found that 25 like tea only and 125 liked c…

03:21

the product of two rational number is- 35/18 if one of the number is 5/12 fi…

01:01

two coins are are tossed simultaneously what is the probability of getting o…

01:50

draw four rectangles of diffrent size each having a perimeter of 16 cm.

(17) There is a narrow rectangular plot, reserved for a school. The length a…