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Homework Help: Antiderivatives (Is my book incorrect?)

  1. Mar 21, 2010 #1
    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)

     
  2. jcsd
  3. Mar 21, 2010 #2

    Doc Al

    User Avatar

    Staff: Mentor

    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.)
     
  4. Mar 21, 2010 #3
    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: May 4, 2017
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