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1.Determine the maximum value of the function f(x)= 5^x -x^5 on the interval 0≤x≤≤2.

2. Determine the minimum value of the function f(x)= e^(-x) - 2e^x on the interval -1≤x≤2.

  • Calculus -

    you know that any local min/max must occur where f' = 0.

    f' = ln5 * 5^x - 4x^2
    That occurs at about x=-.5 and 1.24
    So, check f(x) at the endpoints of the interval, and at those two values.

    Looks to me like max is at x=1.24, min at x=2

    Treat the other similarly.

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