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Math Help - finding values from power functions

  1. #1
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    finding values from power functions

    i have no clue how to do this problem. i need some help.

    Given a power function of the form f(x)=ax^n, with f ' (3)=18 and f ' (6)=72, find n and a .
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by jojoferni244 View Post
    i have no clue how to do this problem. i need some help.

    Given a power function of the form f(x)=ax^n, with f ' (3)=18 and f ' (6)=72, find n and a .
    Find f'(x):

    f'(x)=an x^{n-1}

    Now apply both conditions to this to come up with a system of equations:

    18=3^{n-1}\cdot a\cdot n

    72=6^{n-1}\cdot a\cdot n

    Can you continue?

    --Chris
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    actually im stuck...can you help me please
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  4. #4
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by Chris L T521 View Post
    Find f'(x):

    f'(x)=an x^{n-1}

    Now apply both conditions to this to come up with a system of equations:

    18=3^{n-1}\cdot a\cdot n

    72=6^{n-1}\cdot a\cdot n

    Can you continue?

    --Chris
    Quote Originally Posted by jojoferni244 View Post
    actually im stuck...can you help me please
    Note that 4*18=72

    So we can see that the last equation is 18=\tfrac{1}{4}\cdot6^{n-1}an

    Thus, \tfrac{1}{4}6^{n-1}an=3^{n-1}an\implies \tfrac{1}{4}6^{n-1}=3^{n-1}\implies \tfrac{1}{4}=\frac{3^{n-1}}{6^{n-1}}\implies \tfrac{1}{4}=\left(\tfrac{3}{6}\right)^{n-1} \implies \tfrac{1}{4}=\left(\tfrac{1}{2}\right)^{n-1}\implies \tfrac{1}{4}=\left(\tfrac{1}{2}\right)^{-1}\left(\tfrac{1}{2}\right)^n\implies \tfrac{1}{8}=\left(\tfrac{1}{2}\right)^n

    Can you take it from here? You will find an integer value for n.

    Then plug this into either equation and solve for a.

    --Chris
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