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Increasing function

  1. Apr 25, 2009 #1
    1. The problem statement, all variables and given/known data
    When x=pi/4, the rate at which sinx^2 is increasing is k times the rate at which x is increasing. What is the value of k?
    (answer is 1)


    2. Relevant equations



    3. The attempt at a solution
    I plugged in pi/4 into sinx^2 and i got .5.
    i also took the derivative of sinx^2 and plugged in pi/4 to get the slope, which is 1.
    So it seems to me that I found the rate at which sinx^2 is increasing (1), but i dont know how to find the rate at which x is increasing.
    do i just take an average slope?
     
  2. jcsd
  3. Apr 25, 2009 #2

    dx

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    Hint: (dy/dt) / (dx/dt) = dy/dx.
     
  4. Apr 25, 2009 #3
    i think dy/dt would be 1.
    how do i find dx/dt?
     
  5. Apr 25, 2009 #4

    dx

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    dx/dt is not given and is not needed. You only know that the ratio dy/dt and dx/dt is k. But the ratio of dy/dt and dx/dt is dy/dx, so what does that tell you?
     
  6. Apr 25, 2009 #5
    that it is just simply the slope of sinx^2 when x=pi/4
    which is 1
    ?
     
  7. Apr 25, 2009 #6

    dx

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    Yes, that's right. :smile:
     
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