Problem

Evaluate the second derivative of the given funct…

Problem 30 Easy Difficulty

Evaluate the second derivative of the given function for the given value of $x.$
$$f(x)=x-\frac{2}{x^{3}}, x=-1$$

Answer

24

Related Courses

Calculus 1 / AB

Basic Technical Mathematics with Calculus

Chapter 23

The Derivative

Section 9

Higher Derivatives

Discussion

You must be signed in to discuss.

Top Calculus 1 / AB Educators

Watch More Solved Questions in Chapter 23

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

Video Transcript

In this problem we need to evaluate the second derivative of the function F of X is equal to x minus two, divided by x cube at the point X is equal to minus one. So first of all, that has determined the second derivative of the function For that. Let us rewrite the function as X -2 times X. to the power -3. Then the first derivative of the function will be the derivative of X, which is 1 -2 times the derivative of next to the power minus three, which we can obtain using the power rule as minus three times X. To the power minus three minus one, which is minus four. So what we have is one plus six times X to the power minus four. Next, let us determine the second derivative of F. That would be the derivative of one which is zero because one is a constant plus six times the derivative of X to the power minus four which is minus four times X To the power minus four minus one, which is minus five. So we have minus 24 divided by X to the power five. Now we need to determine the value of the second derivative at the point X equals two minus one, so have double prime minus one will be equal to minus 24 divided by minus one, moved to the power five. We obtain this by substituting X equals two minus one, So this is -24, divided by -1, Which will be equal to 24. Hence the required value is equal to 24.

We have video lessons for 0.06% of the questions in this textbook

Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus

View More Answers From This Book

Find Another Textbook

Problem