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Math Help - Applications involving relative extremum:Finding numbers

  1. #1
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    Unhappy Applications involving relative extremum:Finding numbers

    Find the number in the interval [-1,1] such that the difference of the number minus its square is
    a.) A maximum
    b.) a minimum

    Support your answers graphically.
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  2. #2
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    Quote Originally Posted by ^_^Engineer_Adam^_^ View Post
    Find the number in the interval [-1,1] such that the difference of the number minus its square is
    a.) A maximum
    b.) a minimum

    Support your answers graphically.
    Hello,

    to find an extremum (maximum or minimum) you have to examine the borders of the interval and the drivative of the function.

    Let x be the number you are looking for.

    Then you get the difference by:

    d(x)=x-x^2

    d'(x)=1-2x. If d'(x) = 0 then x = 1/2 and the difference is d(1/2) = 1/4. By the 2nd drivative (it is negative) you know that this must be the maxium.

    Now examine the borders of the given interval:

    d(1) = 0

    d(-1) = -2

    -2 is smaller than 1/4 so this must be the minimum.

    EB
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