Problem

Find $ f $. $ f"(x) = x^3 + \sinh x $, $ \quad…

01:27

Problem 43 Medium Difficulty

Find $ f $.

$ f"(x) = 4 + 6x + 24x^2 $, $ \quad f(0) = 3 $, $ \quad f(1) = 10 $

Answer

$$
f(x)=2 x^{2}+x^{3}+2 x^{4}+2 x+3
$$

Discussion

You must be signed in to discuss.

Top Calculus 2 / BC Educators

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

So picking we have the second derivative of X. And it's equal to four plus six X plus 24 X. Screwed. So when we evaluate this, when you take F prime of X using the anti derivative we get four X plus um free X squared plus. He acts cute Classy. But we know that F of zero is three. So what we're gonna end up getting is Or f of f prime of one is 10. So we're going to end up getting to as R. C value. Then we have F of X. Which is going to give us um to have squared plus X cubed Class two X to the 4th plus two X plus another constant value. But we know that F of zero is three. That means as constant as three. Therefore our final anti derivative is two X squared plus X cubed plus two X. To the fourth plus two X plus three. Final answer.

Carson M.

California Baptist University

Topics

Derivatives

Differentiation

Volume

Calculus: Early Transcendentals

Chapter 4

Applications of Differentiation

Section 9

Antiderivatives

Problem

Find $ f $. $ f"(x) = x^3 + \sinh x $, $ \quad…

Problem 43 Medium Difficulty

Find $ f $.

$ f"(x) = 4 + 6x + 24x^2 $, $ \quad f(0) = 3 $, $ \quad f(1) = 10 $

Answer

$$
f(x)=2 x^{2}+x^{3}+2 x^{4}+2 x+3
$$

More Answers

Topics

Calculus: Early Transcendentals

Discussion

Top Calculus 2 / BC Educators

Kayleah T.

Samuel H.

Michael J.

Joseph L.

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.

Samuel H.

Michael J.

Joseph L.

Calculus 2 / BC Bootcamp

Integration Review - Intro

Definite vs Indefinite

Recommended Videos

Problem

Find $ f $. $ f"(x) = x^3 + \sinh x $, $ \quad…

Problem 43 Medium Difficulty

Find $ f $. $ f"(x) = 4 + 6x + 24x^2 $, $ \quad f(0) = 3 $, $ \quad f(1) = 10 $

Answer

$$f(x)=2 x^{2}+x^{3}+2 x^{4}+2 x+3$$

More Answers

Topics

Calculus: Early Transcendentals

Discussion

Top Calculus 2 / BC Educators

Kayleah T.

Samuel H.

Michael J.

Joseph L.

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.

Samuel H.

Michael J.

Joseph L.

Calculus 2 / BC Bootcamp

Integration Review - Intro

Definite vs Indefinite

Recommended Videos

Find $ f $.

$ f"(x) = 4 + 6x + 24x^2 $, $ \quad f(0) = 3 $, $ \quad f(1) = 10 $

$$
f(x)=2 x^{2}+x^{3}+2 x^{4}+2 x+3
$$