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Thread: Local Maximum Problem

  1. October 29th 2009, 08:59 PM #1
    iheartthemusic29
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    Local Maximum Problem

    Find constants a and b in the function f(x)=axe^(bx) such that f(1/3)=1 and the function has a local maximum at x=1/3.
    Thanks!
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  2. October 30th 2009, 04:28 AM #2
    mr fantastic
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    Quote Originally Posted by iheartthemusic29 View Post
    Find constants a and b in the function f(x)=axe^(bx) such that f(1/3)=1 and the function has a local maximum at x=1/3.
    Thanks!
    Solve the following simultaneously:

    1 = \frac{a}{3} e^{b/3} .... (1)

    f'(1/3) = 0 \Rightarrow a e^{b/3} + \frac{ab}{3} e^{b/3} = 0 .... (2)
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  3. October 30th 2009, 12:28 PM #3
    iheartthemusic29
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    I figured it out.
    a=3e and b=-3
    Thanks!
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« Implicit Differentiation | Multivariable Differentiation Problem »

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