Download the App!

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

For what values of $ x $ does the graph of $ f $ have a horizontal tangent?$ f(x) = x + 2 \sin x $

Get the answer to your homework problem.

Try Numerade free for 7 days

Like

Report

$$(2 n+1) \pi \pm \frac{\pi}{3}, n \text { an integer. }$$

01:21

Frank Lin

Calculus 1 / AB

Chapter 3

Differentiation Rules

Section 3

Derivatives of Trigonometric Functions

Derivatives

Differentiation

Missouri State University

Oregon State University

Harvey Mudd College

Boston College

Lectures

04:40

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.

44:57

In mathematics, a differentiation rule is a rule for computing the derivative of a function in one variable. Many differentiation rules can be expressed as a product rule.

01:23

For what values of $ x $ d…

01:59

03:21

For what values of $x$ doe…

01:22

For what value of $x$ does…

02:01

00:28

For what value of $ x $ do…

03:59

Find all points on the gra…

Hey, it's clear sailing you right here. So we have F of X is equal to X plus to sign, so my first derivatives get one plus to co sign. We know that has a horizontal tangent when the first derivative it's equal to zero. So it's worn plus to co sign is equal to zero. So we get X is equal to two pi thirds or four pi thirds. We put it in the form Texas difficult to two pi over three was two n pi since co sign has a period of two pi Or it could be xs equal to four pipe thirds plus two and pie and is any integer. You realize that these solutions to pie throwers and four pi thirds rpai plus or minus pi over three. So to be written, there's two and prying was pie, plus or minus pi thirds just equal to two end plus one times pi plus or minus 5/3 And is any integer

View More Answers From This Book

Find Another Textbook