Problem

A mass on a spring vibrates horizontally on a smo…

02:21

Problem 34 Medium Difficulty

For what values of $ x $ does the graph of $ f $ have a horizontal tangent?
$ f(x) = e^x \cos x $

Answer

$\pi / 4+k \pi, \quad k \quad \text{is an integer}$

More Answers

00:58

Frank L.

Topics

Derivatives

Differentiation

Book Cover for Calculus: Early Tra…

Calculus: Early Transcendentals

Chapter 3

Differentiation Rules

Section 3

Derivatives of Trigonometric Functions

Discussion

You must be signed in to discuss.

Top Calculus 1 / AB Educators

Catherine R.

Missouri State University

Anna Marie V.

Campbell University

Kayleah T.

Harvey Mudd College

Kristen K.

University of Michigan - Ann Arbor

Watch More Solved Questions in Chapter 3

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

Problem 9

Problem 10

Problem 11

Problem 12

Problem 13

Problem 14

Problem 15

Problem 16

Problem 17

Problem 18

Problem 19

Problem 20

Problem 21

Problem 22

Problem 23

Problem 24

Problem 25

Problem 26

Problem 27

Problem 28

Problem 29

Problem 30

Problem 31

Problem 32

Problem 33

Problem 34

Problem 35

Problem 36

Problem 37

Problem 38

Problem 39

Problem 40

Problem 41

Problem 42

Problem 43

Problem 44

Problem 45

Problem 46

Problem 47

Problem 48

Problem 49

Problem 50

Problem 51

Problem 52

Problem 53

Problem 54

Problem 55

Problem 56

Problem 57

Problem 58

Video Transcript

Hey, it's Claire so immune right here. So we're going to look for values of X. We're gonna start with the derivative. It has to be equal to zero. Since the graph of F has a horizontal attention, you have our original function, which is F of X is equal to eat. The X Times CO sign When we derive this, we're gonna eat. Use a product rule. We end up getting co sign terms each X plus e to X terms Negative sign This makes it equal to co sign next term's Eat the eggs, My nest each the X sign We're gonna take out E to the X We get go sign minus sign We make this equal to zero I mean, we end up getting co sign equals sign so X is equal to pi for plus Kate over Cape I. This is because you were using the reference of the unit circle

Clarissa N.

Topics

Derivatives

Differentiation

Book Cover for Calculus: Early Tra…

Calculus: Early Transcendentals

Chapter 3

Differentiation Rules

Section 3

Derivatives of Trigonometric Functions

Top Calculus 1 / AB Educators

Kayleah T.

Harvey Mudd College

Caleb E.

Baylor University

Kristen K.

University of Michigan - Ann Arbor

Joseph L.

Boston College