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Math Help - critical numbers

  1. #1
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    critical numbers

    Find the critical numbers of the function. f(x) = x^3 + x^2 - x

    whats the smaller value and the larger value?

    the derivative of this is
    3x^2+2x-1 but i get lost right after.
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  2. #2
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    Quote Originally Posted by break View Post
    Find the critical numbers of the function. <i>f</i>(<i>x</i>) = <i>x</i>3 + <i>x</i>2 - <i>x</i>

    whats the smaller value and the larger value?

    the derivative of this is
    3x^2+2x-1 but i get lost right after.
    critical values occur where f'(x) = 0 or where f'(x) is undefined.

    set the above derivative equal to 0 and solve for the critical values of x, then determine extrema.
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  3. #3
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    okay so

    3x^2+2x-1=0
    2x-1=3x^2
    -1=3x^2/2x
    -1=3x/2
    0 = (3x+2)/2

    then

    0 = 3x+2
    -2/3 = x

    not sure if i got this part right.
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  4. #4
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    Quote Originally Posted by break View Post
    Find the critical numbers of the function. f(x) = x^3 + x^2 - x

    whats the smaller value and the larger value?

    the derivative of this is
    3x^2+2x-1 but i get lost right after.

    f(x)=(x^3)+(x^2)-x
    f'(x)=(3x^2)+(2x)-1

    set that equal to zero. you will have to factor the polynomial to get

    (3x-1)(x+1)=0

    so

    3x-1=0
    3x=1
    x=1/3

    x+1=0
    x=-1

    those are your critical values
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  5. #5
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    Quote Originally Posted by skeeter View Post
    critical values occur where f'(x) = 0 or where f'(x) is undefined.

    set the above derivative equal to 0 and solve for the critical values of x, then determine extrema.
    from my understanding, critical values are where f'(x)=0

    partition numbers are where f'(x)=0 or is undefined
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  6. #6
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    Quote Originally Posted by propjohn View Post
    from my understanding, critical values are where f'(x)=0

    partition numbers are where f'(x)=0 or is undefined

    Pauls Online Notes : Calculus I - Critical Points
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