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Math Help - Critical Numbers & Extremas

  1. #1
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    Critical Numbers & Extremas

    Given the equation y=2x^2-8x+9, find the extreme values of the function and where they occur.

    I know I have to find the derivative, then the critical numbers, but when it comes time for the number line, am I plugging numbers into the original equation or the derivative??

    Alsooo, what happens after that?
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  2. #2
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    you are trying to determine the sign of f'(x) for values between critical numbers ...
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  3. #3
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    Quote Originally Posted by skeeter View Post
    you are trying to determine the sign of f'(x) for values between critical numbers ...
    I don't understand.
    See, my teacher told me to first find the derivative, then find the critical numbers, and then make a number line with the critical numbers. So you'd have to pick a number on that line, and plug it in to determine whether you have a max value or min value.
    The problem is, Idk if I plug the number from the number line into the derivative of the equation, or the original equation.

    Did that confuse you?
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  4. #4
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    no, but my response obviously confused you.

    once again ... where will you "plug" in those numbers if you have to determine the sign of f'(x) between the critical values?
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  5. #5
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    ohh.. xD
    now i get it.

    ok, how would i find what the minimum value is at x=2 ?
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  6. #6
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    minimum values occur when f'(x) changes sign from negative to positive ... why?
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  7. #7
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    ok, on the left of the two, i get a neg.. at the right of two, i get a pos.
    so is the min at x=2? or do i have to plug 2 into the original equation?
    because the back of the book says that the min. is at 1.. so idk..
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  8. #8
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    y=2x^2-8x+9 has a minimum at x = 2

    the minimum value is y = 1
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  9. #9
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    ok, but how did you get that the minimum value is at y=1??
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  10. #10
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    plug 2 in for x, calculate the value of y.
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  11. #11
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    Quote Originally Posted by skeeter View Post
    plug 2 in for x, calculate the value of y.

    Thank you very much.
    You've been a huge help for the both of us.
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