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Math Help - A derivative problem?

  1. #1
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    A derivative problem?

    Here's the problem I'm having.

    f(x)=ax^n, where n and a are constants and f'(2)=3 and f'(4)= 24

    I'm totally confused as to what I should be doing of even what the first steps should be. Any help is greatly appreciated.
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by _nysa View Post
    Here's the problem I'm having.

    f(x)=ax^n, where n and a are constants and f'(2)=3 and f'(4)= 24

    I'm totally confused as to what I should be doing of even what the first steps should be. Any help is greatly appreciated.
    they want you to find the constants a and n

    find the derivative, then, plug in the values as prescribed. you will obtain two equations in a and n that you can solve simultaneously
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  3. #3
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    they want you to find the constants a and n

    find the derivative, then, plug in the values as prescribed. you will obtain two equations in a and n that you can solve simultaneously
    Maybe I'm being slow here, but when I do a derivative I get:

    a(nx^n-1)

    And this is the part where I get confused, because I don't know what values go where.
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  4. #4
    Rhymes with Orange Chris L T521's Avatar
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    A similar problem was done here.

    --Chris
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  5. #5
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    Thanks Chris, but I'm stuck again.

    I followed the example that you linked too, and this is what I got to.

    1/8 = (1/8)^-1(1/8)^n

    And then I don't know what to do anymore.
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  6. #6
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by _nysa View Post
    Thanks Chris, but I'm stuck again.

    I followed the example that you linked too, and this is what I got to.

    1/8 = (1/8)^-1(1/8)^n

    And then I don't know what to do anymore.
    Well, \left(\tfrac{1}{8}\right)^{-1}=8

    So we have \tfrac{1}{8}=8\cdot\left(\tfrac{1}{8}\right)^n

    This implies \tfrac{1}{64}=\left(\tfrac{1}{8}\right)^n

    Can you finish this?

    [hint: 64=8^2]

    --Chris
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  7. #7
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    Yes I can, thanks so much!
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