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Homework Help: Weird result to a simple derivative question

  1. Jun 21, 2011 #1


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    I am told to write the value of a the derivative at a certain point next to each function. And to find the point/s

    f(x) = x2

    f ' (x) = -6

    so I figured I just do

    f ' (x) = 2x

    f ' (-6) = 2 x (-6) = -12

    But they tell me the answer is

    (-3, 9)
  2. jcsd
  3. Jun 21, 2011 #2

    Char. Limit

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    The problem is that f'(x)=-6, and what you plugged in is equivalent to x=-6.

    You got the derivative right, but you need to set f'(x) to -6, not x.
  4. Jun 21, 2011 #3


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    Oh... I see! thanks :)
  5. Jun 23, 2011 #4


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    Another way to look at it....
    You were given value of the derivative
    [itex]f'(x) = -6[/itex] (eq 1)
    and you found the derivative of equation [itex]f(x)=x^2[/itex] to be
    [itex]f'(x) = 2x[/itex] (eq 2)

    The left side of equations 1 & 2 are equal,
    therefore the right sides are also,
    so -6 = 2x and you can solve for x.

    To find y, substitute this x into the original equation of f(x)
    and you will obtain the same point you noted from the solution guide.
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