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Math Help - Stuck on absolute extrema problem

  1. #1
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    Stuck on absolute extrema problem

    Find locations (ordered pairs) of all absolute extrema for the following function with the specific domain.

    f(x)= \frac{1-x}{3+x} Domain: [0,3]
    f'(x)=\frac{(3+x)(-1)-(1-x)(1)}{(3+x)^2}

    What do i do after this to find the absolute extrema (min,max)

    Thanks!
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  2. #2
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by Jim Marnell View Post
    Find locations (ordered pairs) of all absolute extrema for the following function with the specific domain.

    f(x)= \frac{1-x}{3+x} Domain: [0,3]
    f'(x)=\frac{(3+x)(-1)-(1-x)(1)}{(3+x)^2}

    What do i do after this to find the absolute extrema (min,max)

    Thanks!
    Note that your derivative simplifies to f^{\prime}\!\left(x\right)=-\frac{4}{\left(x+3\right)^2}

    Since f^{\prime}\!\left(x\right) never equals zero, we must consider where it is undefined. This is when x+3=0\implies x=-3. Since -3\notin\left[0,3\right] we can't consider it to be a critical point.

    Since the interval of interest is a closed interval, consider the value of the function at the endpoints:

    f\!\left(0\right)=\frac{1}{3}

    f\!\left(3\right)=-\frac{2}{9}

    Thus, the absolute maximum is at \left(0,\tfrac{1}{3}\right) and the absolute minimum is at \left(3,-\tfrac{2}{9}\right).

    Does this make sense?
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  3. #3
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    Thanks, I understand how to figure these problems out now!
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