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Thread: Finding maximum

  1. #1
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    Finding maximum

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

    Find y max

    Here is how I'm approaching this ...

    $\displaystyle 6x-x^2$

    $\displaystyle y'=6-2x$

    With 3 being a critical point

    $\displaystyle y''=-2$

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

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

    But I see what you were trying to do.

    It should be,

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

    $\displaystyle 2y = 6x - x^2$

    $\displaystyle 2y' = 6 - 2x$

    $\displaystyle y' = 3 - x$

    I know, the root doesn't change by multiplication or division, but $\displaystyle y' = 6-2x$ 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 ...

    $\displaystyle y''=-1$

    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 $\displaystyle 3x-\frac{x^{2}}{2}$?.

    Did you just differentiate?.

    $\displaystyle y'=3-x$

    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 $\displaystyle x=3$ and the maximum value of the function is $\displaystyle f(3) = 9/2$ as galactus said? If you know it, no problem
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  6. #6
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    You can also find this without calc by using $\displaystyle x=\frac{-b}{2a}$.

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

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

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

    The equation wanted "y max," not "x max" so technically it is $\displaystyle \frac{9}{2}$ 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" $\displaystyle \frac{9}{2}$. Evil questions. Thanks for catching that
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