Problem

Find equations of the tangent line and normal lin…

01:47

Problem 37 Medium Difficulty

Find equations of the tangent line and normal line to the curve at the given point.
$ y = x^4 + 2e^x, (0,2) $

Answer

$$y-2=-\frac{1}{2}(x-0) \text { or } y=-\frac{1}{2} x+2$$

More Answers

01:38

Frank L.

Topics

Derivatives

Differentiation

Book Cover for Calculus: Early Tra…

Calculus: Early Transcendentals

Chapter 3

Differentiation Rules

Section 1

Derivatives of Polynomials and Exponential Functions

Discussion

You must be signed in to discuss.

Top Calculus 1 / AB Educators

Grace H.

Kayleah T.

Harvey Mudd College

Caleb E.

Baylor University

Joseph L.

Boston College

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

Problem 59

Problem 60

Problem 61

Problem 62

Problem 63

Problem 64

Problem 65

Problem 66

Problem 67

Problem 68

Problem 69

Problem 70

Problem 71

Problem 72

Problem 73

Problem 74

Problem 75

Problem 76

Problem 77

Problem 78

Problem 79

Problem 80

Problem 81

Problem 82

Problem 83

Problem 84

Problem 85

Problem 86

Video Transcript

it's clear. So when you right here. So we have y is equal to X to the fourth plus to eat tax. We're gonna differentiate, do you? I over d x and we get d over t X in terms of X for X to the fourth plus to eat the axe. This gives us four X cute plus to eat the axe in the slope of the tangent at zero comma, too. It is going to be, too, because when we plug in zero, this cross is out and this becomes just to so it's too. So the slope of the normal line has to be negative 1/2 since the product of slopes of perpendicular lines is negative. One. The tangent is the line. Passing through 02 was slope too. So the equation is lie minus two over X minus zero is equal to two. We get why it's equal to two acts plus two, and the normal is the line passing through 02 with slope negative 1/2. So the equation is boy minus two over X minus. Cerro is equal to negative 1/2. Why is equal to negative 1/2 X plus two. So this is our tangent, and this is our normal

Clarissa N.

Topics

Derivatives

Differentiation

Book Cover for Calculus: Early Tra…

Calculus: Early Transcendentals

Chapter 3

Differentiation Rules

Section 1

Derivatives of Polynomials and Exponential Functions

Top Calculus 1 / AB Educators

Grace H.

Numerade Educator

Kayleah T.

Harvey Mudd College

Caleb E.

Baylor University

Joseph L.

Boston College