Problem

The graph of a function $ f $ is shown. Which gra…

02:42

Problem 50 Medium Difficulty

Find a function $ f $ such that $ f'(x) = x^3 $ and the line $ x + y = 0 $ is tangent to the graph of $ f $.

Name: find a function f such that fx x3 and the line x y 0 is tangent to the graph of f
Uploaded: 2019-11-18
Duration: 48 s
Channel: Numerade
Description: Find a function $ f $ such that $ f'(x) = x^3 $ and the line $ x + y = 0 $ is tangent to the graph of $ f $.

Answer

$$
f(x)=\frac{1}{4} x^{4}+\frac{3}{4}
$$

Discussion

You must be signed in to discuss.

Top Calculus 2 / BC Educators

Kayleah T.

Harvey Mudd College

Caleb E.

Baylor University

Kristen K.

University of Michigan - Ann Arbor

Michael J.

Idaho State University

Watch More Solved Questions in Chapter 4

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

Video Transcript

we know we're trying to find the X coordinate when the derivative equals negative one There for Alexa X cubed equal to negative one we get AKs is negative one to the power of 1/3 which is negative one. Therefore, using the tangent line Why is negative x negative negative. Want which is positive one. Therefore, if after backs is 1/4 axe to the fourth proceed may get one is 1/4 times negative one Combats are acts in this context to the fourth pussy giving us 3/4 equal. See, giving us a function after box is one fork extra fourth plus three divide by four

Amrita B.

Topics

Derivatives

Differentiation

Volume

Calculus: Early Transcendentals

Chapter 4

Applications of Differentiation

Section 9

Antiderivatives

Problem

The graph of a function $ f $ is shown. Which gra…

Problem 50 Medium Difficulty

Find a function $ f $ such that $ f'(x) = x^3 $ and the line $ x + y = 0 $ is tangent to the graph of $ f $.

Answer

$$
f(x)=\frac{1}{4} x^{4}+\frac{3}{4}
$$

More Answers

Topics

Calculus: Early Transcendentals

Discussion

Top Calculus 2 / BC Educators

Kayleah T.

Caleb E.

Kristen K.

Michael J.

Calculus 2 / BC Bootcamp

Integration Review - Intro

Definite vs Indefinite

Recommended Videos

Watch More Solved Questions in Chapter 4

Video Transcript

Topics

Calculus: Early Transcendentals

Top Calculus 2 / BC Educators

Kayleah T.

Caleb E.

Kristen K.

Michael J.

Calculus 2 / BC Bootcamp

Integration Review - Intro

Definite vs Indefinite

Recommended Videos

Problem

The graph of a function $ f $ is shown. Which gra…

Problem 50 Medium Difficulty

Find a function $ f $ such that $ f'(x) = x^3 $ and the line $ x + y = 0 $ is tangent to the graph of $ f $.

Answer

$$f(x)=\frac{1}{4} x^{4}+\frac{3}{4}$$

More Answers

Topics

Calculus: Early Transcendentals

Discussion

Top Calculus 2 / BC Educators

Kayleah T.

Caleb E.

Kristen K.

Michael J.

Calculus 2 / BC Bootcamp

Integration Review - Intro

Definite vs Indefinite

Recommended Videos

Watch More Solved Questions in Chapter 4

Video Transcript

Topics

Calculus: Early Transcendentals

Top Calculus 2 / BC Educators

Kayleah T.

Caleb E.

Kristen K.

Michael J.

Calculus 2 / BC Bootcamp

Integration Review - Intro

Definite vs Indefinite

Recommended Videos

$$
f(x)=\frac{1}{4} x^{4}+\frac{3}{4}
$$