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Math Help - Global Extremas

  1. #1
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    Global Extremas

    Find the global extrema of the function f(x,y) = sin(xy) on the closed region given by 0 \leq\ x \leq \pi and 0 \leq\ y \leq 1. Be sure to clearly indicate the maximum and minimum vlues and where they occur.

    Thanks!!
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  2. #2
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    I'm still waiting for your partial derivatives and why you think that bore no fruit. Did you investigate those boundaries, yet?
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  3. #3
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    Quote Originally Posted by TKHunny View Post
    I'm still waiting for your partial derivatives and why you think that bore no fruit. Did you investigate those boundaries, yet?
    I tested the boundaries and I think the only critical point I got was (\pi/2, 1).

    I found critical points from the partial derivaties and I think the points are (0,0), (0, 1/2), (\pi, 1/2).

    I think those are all the critical points.
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  4. #4
    is up to his old tricks again! Jhevon's Avatar
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    Here's how to classify the critical points. I think you got all of them...how did you get (0,1/2)?

    Define D(a,b) = f_{xx}(a,b) f_{yy} - [f_{xy}(a,b)]^2

    where (a,b) is a critical point.

    Here are the rules:

    1. If D > 0 and f_{xx}(a,b) > 0, then f(a,b) is a local minimum

    2. If D > 0 and f_{xx}(a,b) < 0, then f(a,b) is a local maximum

    3. If D < 0, then f(a,b) is a saddle point (neither a max or min)

    those are all the points you got from the boundary?
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  5. #5
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    Quote Originally Posted by TKHunny View Post
    I'm still waiting for your partial derivatives and why you think that bore no fruit. Did you investigate those boundaries, yet?
    I finished the problem and I got...
    maximums (\pi, 1/2) and (\pi/2, 1)
    no minimums

    I don't know if this is right.
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