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Math Help - Absolute max and min

  1. #1
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    Smile Absolute max and min

    Find the absolute max and min values of the function, if they exist, over the indicated interval.

    F(x) = x (square root of x+3) ; [-3,6]
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  2. #2
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    Quote Originally Posted by littlesohi View Post
    Find the absolute max and min values of the function, if they exist, over the indicated interval.

    F(x) = x (square root of x+3) ; [-3,6]
    f(x)=x\sqrt{x+3}

    f'(x)=\frac{x}{2\sqrt{x+3}}+\sqrt{x+3}

    =\frac{3x+6}{2\sqrt{x+3}}

    The critical numbers are given by

    3x+6=0

    x=-2

    So f(-2) should be an extreme point.

    So to determine whether it's a max or min you can just examine points write around f(-2) and see if they are less than or great than f(-2).
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