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Find a point given a derivative and a point.

  1. Nov 1, 2013 #1


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    1. The problem statement, all variables and given/known data

    http://i2.minus.com/jyK7QefQtK8Ul.png [Broken]

    2. Relevant equations

    Point-slope form of a line.

    y - y1 = m(x - x1)

    3. The attempt at a solution

    I'm assuming this is the correct approach to this problem (see below):

    http://i4.minus.com/ibnDPl1kiE2f6p.jpg [Broken]
    Last edited by a moderator: May 6, 2017
  2. jcsd
  3. Nov 1, 2013 #2
    The question requires you to solve the differential equation f'(x)=2-4/sqrt(x). What you are calculating is the tangent line at any point.
  4. Nov 1, 2013 #3


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    Solving the differential ... is this what you mean?
  5. Nov 1, 2013 #4
    What you just did doesn't make any sense. Even if you haven't yet learned solving the differential equations, this one isn't really hard.

    You have dy=(2-4/sqrt(x))dx. You simply need to integrate both the sides.
  6. Nov 1, 2013 #5


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    Alright, I integrate and I get y = 2x - (8)x^(1/2)

    This is odd since I don't think we've learned integration yet. I know it, but ...

    I suppose y = 8 - 8(2) = -8?
  7. Nov 1, 2013 #6


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    What I did I think was linearization and I found the change in y (dy). Knowing how much y changed from the original y-coordinate of the point can help me find the new y.

    I think. I'm waiting to be either corrected or affirmed.
  8. Nov 1, 2013 #7
    Almost but you missed the constant of integration. You need to use the given information to find the constant.
  9. Nov 1, 2013 #8


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    When you integrate, you also get the constant of integration, so you should have y = f(x) = 2x - 8√x + C. You're given that the point (1, -2) is on the graph of f, so you can solve for C.
  10. Nov 1, 2013 #9


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    Oh good point. The constant should be 4.

    -2 = 2 - 8(1) + c = -6 + c.

    So my original answer is off by 4. The answer I suppose is -4? C?
  11. Nov 1, 2013 #10
    No. You are still not done. Now that you have found the constant, write f(x) and evaluate f(4).

    EDIT: Yes, the answer is -4, that's what I get.
  12. Nov 1, 2013 #11


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    Yes, and it's -4.

    y = 2(4) - 8(2) + 4 = 8 - 16 + 4 and that's -8 plus 4 = -4.

    Thanks guys for reminding me about integration! I c now! :).
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