Calculus

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Find the absolute maximum value and the absolute minimum value,
g(x)=1/8 x^2 - 4 x^(1/2) on [0, 9]

  • Calculus -

    g'(x) = x/4 - 2x^(-1/2) = x/4 - 2/√x
    = 0 for a max/min

    x/4 = 2/√x
    x^(3/2) = 8
    x = 8^(2/3) = 4
    then f(4) = 2 - 4(2) = -6

    for endpoints:
    f(0) = 0
    f(9) = 81/8 - 12 = -15/8 = -1.875

    so within the given domain, the maximum function value is 0 , when x = 0

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