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Math Help - find derivative then solve for x

  1. #1
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    find derivative then solve for x

    f(x)= (x^3)lnx

    f'(x) = (3x^2)(lnx) +(x^3)(1/x)
    = (3x^2)lnx + x^2
    = x^2(3lnx+1)

    x^2 = 0
    x=0

    3lnx +1 =0
    lnx =-1/3

    x=e^(-1/3)

    is my work all correct?

    I was able to find find f''(x) of x^2(3lnx+1) so I don't know.
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  2. #2
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    Re: find derivative then solve for x

    What is your ultimate goal with this problem? What are you trying to determine?
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  3. #3
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    Re: find derivative then solve for x

    I am trying to find out where f interval increase and decrease.

    so far I have

    INCREASE: ( __ , infinity)

    DECREASE: ( 0, __ )
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  4. #4
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    Re: find derivative then solve for x

    Quote Originally Posted by NeoSonata View Post
    f(x)= (x^3)lnx

    f'(x) = (3x^2)(lnx) +(x^3)(1/x)
    = (3x^2)lnx + x^2
    = x^2(3lnx+1)

    x^2 = 0
    x=0

    3lnx +1 =0
    lnx =-1/3

    x=e^(-1/3)

    is my work all correct?
    Yeh, this looks good, now graph the function using technology, is \displystyle  \frac{1}{\sqrt[3]{e}}\approx 0.72 in the neighbourhood of your turning point?
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  5. #5
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    Re: find derivative then solve for x

    yeah..

    ___________________
    0 ---- .72 ++++++


    so it should be increasing from (.72, infinity) and decreasing from (0, .72) ?

    web-assign will not accept so probably the system is incorrect.
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  6. #6
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    Re: find derivative then solve for x

    Quote Originally Posted by NeoSonata View Post

    so it should be increasing from (.72, infinity) and decreasing from (0, .72) ?
    That's how I see it.
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  7. #7
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    Re: find derivative then solve for x

    Maybe WebAssign needs more digits for accuracy, or maybe it needs the exact result.
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  8. #8
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    Re: find derivative then solve for x

    It might do, I'm not aware of this software.

    If you were doing a written exam the exact value of e^(-1/3) will always be best.
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