• Support PF! Buy your school textbooks, materials and every day products Here!

Antiderivatives (Is my book incorrect?)

  • Thread starter 01010011
  • Start date
  • #1
48
0
Is my working correct, or is my math pdf (in red font) correct?

1. The problem statement: Find f(x) given that f′′(x) = 3/squareroot of x, f(4) = 20 and
f′(4) = 7.


2. Most General Antiderivative: F(X) + C

3. The Attempt at a Solution

First, simplify 3/squareroot of x:

= 3x^(-1/2)

Next, most general antiderivative = F(x) + C

= [3x^(-1/2 + 1)] / [-1/2 + 1] + C

= [3x^1/2] / [1/2] + C

= 2 * 3x^1/2 + C

= 6x^1/2 + C

Now, f′(4) = 6x^1/2 + C = 7

= 6(4)^1/2 + C = 7 (The pdf has: f′(4) = 6 · 2 + C = 7 so C = −1. )

= 6(2) + C = 7

= 12 + C = 7

C = 7 - 12

C = -5

= f′(x) = 6x^(1/2) − 5 (The pdf has:f′(x) = 6x^(1/2) − 1. )

= [6x^(3/2)] / (3/2) - 5x + C

= 2/3 * 6x^ 3/2 - 5x + C

= 4x^3/2 -5x + C

f(4) = 4(4)^3/2 - 5(4) + C = 20

4 * 8 - 20 + C = 20

C = 20 - 32 + 20

C = 8

Therefore, f(x) = 4x^3/2 - 5x + C (The pdf has:f(x) = 4x^(3/2)− x)

 

Answers and Replies

  • #2
Doc Al
Mentor
44,904
1,169
Is my working correct, or is my math pdf (in red font) correct?
Your work is correct; the pdf is not. (You can check by working backwards and by plugging in the constraints and seeing if they are met.)
 
  • #3
48
0
Your work is correct; the pdf is not. (You can check by working backwards and by plugging in the constraints and seeing if they are met.)
Thank you Doc Al.

I thought that since the pdf is from Portland University, it would have been reliable. However, it was still very helpful because it explained how to do antiderivatives.
Here is the link:
http://faculty.up.edu/wootton/Calc1/Section4.9.pdf" [Broken]
 
Last edited by a moderator:

Related Threads on Antiderivatives (Is my book incorrect?)

Replies
9
Views
1K
Replies
2
Views
983
Replies
8
Views
794
  • Last Post
Replies
10
Views
837
  • Last Post
Replies
4
Views
2K
  • Last Post
Replies
8
Views
2K
  • Last Post
Replies
15
Views
999
  • Last Post
Replies
7
Views
3K
  • Last Post
Replies
2
Views
1K
  • Last Post
Replies
3
Views
1K
Top