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Thread: 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
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    First, derive the function:

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

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

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


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

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

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

    $\displaystyle 36 = 12ae^{-1}$

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