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Math Help - derivatives

  1. #1
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    derivatives

    what is the first and second derivative of:

    f(x) = (x^(2/3))(x-5)
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  2. #2
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    Hello,

    (x^{2/3})(x-5)=x^{5/3}-5x^{2/3}


    The derivative for x^a is ax^{a-1}

    This is all you need...
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  3. #3
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    i need a little more help

    for the first derivative i got f'(x) = (5/3)(x^(2/3)) - (10/3)(x^(-1/3))...... but i need to be able to get the critical numbers for this and i can't figure out what they are. I know i am suppose to set the equation equal to 0 but i still can't get it. And i have to show my work so I'm not suppose to use a calculator.
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  4. #4
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    The first derivative is correct

    Solve for x in :
    f'(x) = (5/3)(x^{2/3}) - (10/3)(x^{-1/3})=0

    \frac{5}{3} x^{2/3}-\frac{10}{3} \frac{1}{x^{1/3}}=0

    Assuming that x is different from 0 (from the beginning ^^)

    Multiply both sides by x^(1/3)

    \frac{5}{3} x^{2/3+1/3}-\frac{10}{3}=0

    \frac{5}{3} x - \frac{10}{3}=0

    Do you see the critical point ? ^^
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  5. #5
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    yes thank you...

    Now i'm having trouble with the 2nd derivative... if i have f'(x) = (5/3)(x^(2/3)) - (10/3)(x^(-1/3))... then does the 2nd derivative f"(x) = (10/9)(x^(-1/3)) + (10/9)(x^(-4/3)) ???
    Last edited by smschaefer; April 13th 2008 at 09:56 AM. Reason: need more help
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