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Math Help - Finding maximum

  1. #1
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    Finding maximum

    y=3x-\frac{x^2}{2}

    Find y max

    Here is how I'm approaching this ...

    6x-x^2

    y'=6-2x

    With 3 being a critical point

    y''=-2

    So the critical point is a maximum. It's a parabola opening downward from 3?
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  2. #2
    Super Member wingless's Avatar
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    We have y = 3x - \frac{x^2}{2}

    But
    6x-x^2 ??
    y' = 6-2x ??
    These are wrong.

    But I see what you were trying to do.

    It should be,

    y = 3x - \frac{x^2}{2}

    2y = 6x - x^2

    2y' = 6 - 2x

    y' = 3 - x

    I know, the root doesn't change by multiplication or division, but y' = 6-2x is not correct.
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  3. #3
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    Thank you for clarifying. I'm prone to making mistakes and that is why I like to double check. Looking at the equation is still seems 3 is our critical point, but the differences in our y' will become ...

    y''=-1

    Which should still give us 3 as our maximum with a downward opening parabola. I appreciate the help as this mistake could have cost me in other equations
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  4. #4
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    Are you just trying to find the max of 3x-\frac{x^{2}}{2}?.

    Did you just differentiate?.

    y'=3-x

    3-x=0, x=3

    That gives y=9/2 as the max value for y.

    If I am misunderstanding, I apologize.
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  5. #5
    Super Member wingless's Avatar
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    Quote Originally Posted by XIII13Thirteen View Post
    Which should still give us 3 as our maximum with a downward opening parabola. I appreciate the help as this mistake could have cost me in other equations
    Do you know that the maximum is at x=3 and the maximum value of the function is f(3) = 9/2 as galactus said? If you know it, no problem
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  6. #6
    Eater of Worlds
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    You can also find this without calc by using x=\frac{-b}{2a}.

    Which gives the x-coordinate for the vertex of a parabola.

    In your case, a=-1/2 and b=3

    \frac{-3}{2(\frac{-1}{2})}=3
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  7. #7
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    Your correct.

    The equation wanted "y max," not "x max" so technically it is \frac{9}{2} is correct. I'm doing these equations with a multiple choice solution set and he has

    a.)4

    b.)3

    c.)-1

    d.)none of these

    I originally picked b because I was thinking of in terms of x, but in the context of "find y max" \frac{9}{2}. Evil questions. Thanks for catching that
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