Refer a friend and earn $50 when they subscribe to an annual planRefer Now

Get the answer to your homework problem.

Try Numerade Free for 30 Days

Like

Report

Let $f(x)=x e^{2 x}$a. Find the values of $x$ for which the slope of the curve $y=f(x)$ is 0b. Explain the meaning of your answer to part (a) in terms of the graph of $f$

a. $x=-\frac{1}{2} \quad$ b. The line tangent to the graph of $f(x)$ at $x=-\frac{1}{2}$ is horizontal.

Calculus 1 / AB

Chapter 3

Derivatives

Section 7

The Chain Rule

Differentiation

Missouri State University

Harvey Mudd College

University of Michigan - Ann Arbor

Idaho State University

Lectures

03:09

In mathematics, precalculu…

31:55

In mathematics, a function…

02:03

Finding slope locations Le…

06:06

a. Graph the function $f(x…

02:22

Suppose the graph of $f$ i…

01:29

02:42

Graph the parabola $f(x)=x…

02:23

Let $ f(x) = \sqrt{1 - x^2…

06:20

a. Find $f^{-1}(x)$b. …

07:25

(a) Sketch the graph of th…

03:03

The graph of $ f $ is give…

01:51

Use the accompanying graph…

okay, So because we have two functions that are multiplying with each other in order to be active in derivative, we need to use the product rule, which states that first, to keep the first term constant and take the derivative of the second term into the power to X, which is each of the power to extend to plus. Then you keep the second term constant and take the derivative of the first term. Next, we can simplify this by taking D to the Part two X. There's a common factor on your love toy this two x plus one inside the parentheses. In order to get the point at which the ingredient is zero, we set the derivative equal to zero. So has your legal two X plus one. Thereby X is equal to minus half For the second part. Let's find the value of why when X is equal to minus absolutely substitutes. Why into our equation X to the power to eggs. So we'll have minus half E to the policy to Linz minus half. Then this gives us marinas wouldn't over to you. So basically what this means is that at the point minus half on minus one over to e be tangent is horizontal, where the Grady Int zero

View More Answers From This Book

Find Another Textbook

In mathematics, precalculus is the study of functions (as opposed to calculu…

In mathematics, a function (or map) f from a set X to a set Y is a rule whic…

Finding slope locations Let $f(x)=x e^{2 x}$a. Find the values of $x$ fo…

a. Graph the function $f(x)=\left\{\begin{array}{ll}x & \text { if } x \…

Suppose the graph of $f$ is given. Describe how the graph of each function c…

Graph the parabola $f(x)=x^{2} .$ Explain why the secant lines between the p…

Let $ f(x) = \sqrt{1 - x^2} $ , $ 0 \le x \le 1 $.

(a) Find $ f^{-1}…

a. Find $f^{-1}(x)$b. Graph $f$ and $f^{-1}$ together.c. Evaluate $d…

(a) Sketch the graph of the function $ f(x) = x | x | $.(b) For what val…

The graph of $ f $ is given. Use it to graph the following functions.

Use the accompanying graph of $y=f(x)$ below to sketch a graph of each equat…

02:33

Evaluate $\int a \cos x \, d x$ and $\, \int a \sin x \, d x,$ where $a$ is …

04:01

Logarithmic differentiation Use logarithmic differentiation to evaluate $f…

00:23

Use the guidelines of this section to make a complete graph of $f$.$$f(x…

01:17

Give the antiderivatives of $x^{p}$. For what values of $p$ does your answer…

04:30

Absolute maxima and minima Determine the location and value of the absolute …

05:01

03:10

Of all rectangles with a fixed perimeter of $P,$ which one has the maximum a…

02:21

Locating critical points Find the critical points of the following functions…

05:47

A camera is set up at the starting line of a drag race 50 fe from a dragster…

04:45

92% of Numerade students report better grades.

Try Numerade Free for 30 Days. You can cancel at any time.

Annual

0.00/mo 0.00/mo

Billed annually at 0.00/yr after free trial

Monthly

0.00/mo

Billed monthly at 0.00/mo after free trial

Earn better grades with our study tools:

Textbooks

Video lessons matched directly to the problems in your textbooks.

Ask a Question

Can't find a question? Ask our 30,000+ educators for help.

Courses

Watch full-length courses, covering key principles and concepts.

AI Tutor

Receive weekly guidance from the world’s first A.I. Tutor, Ace.

30 day free trial, then pay 0.00/month

30 day free trial, then pay 0.00/year

You can cancel anytime

OR PAY WITH

Your subscription has started!

The number 2 is also the smallest & first prime number (since every other even number is divisible by two).

If you write pi (to the first two decimal places of 3.14) backwards, in big, block letters it actually reads "PIE".

Receive weekly guidance from the world's first A.I. Tutor, Ace.

Mount Everest weighs an estimated 357 trillion pounds

Snapshot a problem with the Numerade app, and we'll give you the video solution.

A cheetah can run up to 76 miles per hour, and can go from 0 to 60 miles per hour in less than three seconds.

Back in a jiffy? You'd better be fast! A "jiffy" is an actual length of time, equal to about 1/100th of a second.