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Thread: Calc 3 - Extreme Values and Saddle points

  1. #1
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    Calc 3 - Extreme Values and Saddle points

    Not sure where to start. I'm on 63a.. I think I'm supposed to solve f(x,y) = x+y and x^2+y^2 = 4 for y giving me y = -x and y = sqrt(4-x^2) and then graph those two but I'm not sure what to do next.

    I could be completely wrong also.

    https://imgur.com/a/lzrShWV
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  2. #2
    Junior Member Walagaster's Avatar
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    Re: Calc 3 - Extreme Values and Saddle points

    Quote Originally Posted by MrJank View Post
    Not sure where to start. I'm on 63a.. I think I'm supposed to solve f(x,y) = x+y and x^2+y^2 = 4 for y giving me y = -x and y = sqrt(4-x^2) and then graph those two but I'm not sure what to do next.

    I could be completely wrong also.

    https://imgur.com/a/lzrShWV
    No, that isn't what you want to do. Use the hint $x=2\cos t,~y = 2\sin t$. Put that in $f = x+y$ to get a function of $t$. Then you have a one variable problem on the appropriate $t$ interval.
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    Re: Calc 3 - Extreme Values and Saddle points

    So, I use x=2cost and y = 2sint and get 2cost + 2sint for that equation. So then I would take the derivative of that and get the critical points? I'm not sure where the equations for the semi and quarter circles come in to play.
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  4. #4
    Junior Member Walagaster's Avatar
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    Re: Calc 3 - Extreme Values and Saddle points

    Quote Originally Posted by MrJank View Post
    So, I use x=2cost and y = 2sint and get 2cost + 2sint for that equation. So then I would take the derivative of that and get the critical points? I'm not sure where the equations for the semi and quarter circles come in to play.
    You have to check which values of $t$ give the semi or quarter circles. And don't forget you have to check the end points of the $t$ intervals for possible max/mins.
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