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Math Help - Critical number?

  1. #1
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    Critical number?

    Determine all of the critical numbers of the given function.

    I'm like 90% sure that means solve for x, check if what you got for x actually works, and that/those are your critical number(s).

    Anyways, here's the problem:

    g(x) = x - \sqrt{14-x} - 2

    Any ideas anyone? I tried solving for x:

    0 = x-\sqrt{14-x} - 2

    then
    \sqrt{14-x} = x-2

    then squared both sides
    14-x = x^2-4

    then moved some stuff around
    18 = x^2+x

    and now I'm stuck there, not even knowing if I'm supposed to be doing this.

    HALP
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  2. #2
    MHF Contributor
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    Quote Originally Posted by DHS1 View Post
    Determine all of the critical numbers of the given function.

    I'm like 90% sure that means solve for x, check if what you got for x actually works, and that/those are your critical number(s).

    Anyways, here's the problem:

    g(x) = x - \sqrt{14-x} - 2

    Any ideas anyone? I tried solving for x:

    0 = x-\sqrt{14-x} - 2

    then
    \sqrt{14-x} = x-2

    then squared both sides
    14-x = x^2-4 ... mistake here, corrected below
    14 - x = x^2 - 4x + 4

    0 = x^2 - 3x - 10

    0 = (x - 5)(x + 2)

    x = 5 ... x = -2

    check both solutions in the original equation
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  3. #3
    Member Mentia's Avatar
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    also remember that if the factorization isnt obvious that you can always use the quadratic equation.
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