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Math Help - Find values of a and b so that the function has a local maximum

  1. #1
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    Find values of a and b so that the function has a local maximum

    Find values of a and b so that the function has a local maximum at the point (12, 36).

    f(x) = axe^(bx)

    I really am just confused on how to do this.

    Thanks in advance,

    Tyler
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  2. #2
    Junior Member
    Joined
    Oct 2009
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    First, derive the function:

    f'(x) = ae^{bx} + abxe^{bx} = e^{bx}(a + abx)

    Now, for stationary points, the derivative must equal 0.

    So 0 = e^{bx}(a+ abx)


    Since e^{bx} can never equal 0, we must have (a + abx) = 0   \therefore x = \frac{-1}{b}

    For the stationary point to be at 12, we must have 12 = \frac{-1}{b}   \therefore b = \frac{-1}{12}

    Going back to the original function, we must now have:

    36 = 12ae^{-1}

    3 = \frac{a}{e}    \therefore a = 3e
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