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Another Calculus

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Sorry I have been trying to figure this out all day. Find the largest and smallest values of the given function over the prescribed closed, bounded interval.
g(t)= (t^3/2)(e^-2t) for 0<t<1.

  • Another Calculus - ,

    Using the product rule
    g'(t) = t^(3/2)(-2)e^(-2t) + (3/2)t^(1/2)(e^(-2t))
    common factor ...
    = (1/2)e^(-2t)(t^(1/2)) [-4t + 3}

    set this equal to zero
    from the first factor we get t=0
    and from the second one we get t = 3/4

    now evaluate
    g(0) = ..
    g(3/4) = ..
    g(1) = ...

    and determine which is the largest and smallest value.

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