course mth 272 s[ƠiӇassignment #030
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08:30:13 Query problem 7.5.10 extrema of x^2+6xy+10y^2-4y+4
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RESPONSE --> first, you need to find the partial derivatives fx(x,y) = 2x + 6y fy(x,y) = 6x + 20y - 4 the only critical points are those for which the first partial derivatives are zero. i'm not sure how you'd set something equal to zero though that has 2 different variables. fxx(x,y) = 2 fyy(x,y) = 20 fxy(x,y) = 6 so (2)(20) - 6 = 34 and is a relative minimum confidence assessment: 2
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08:34:44 List the relative extrema and the saddle points of the function and tell which is which, and how you obtained each.
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RESPONSE --> I already listed the relative minimum saddle points: alright, I think when ou set 2x + 6y equal to 0 and 6x + 20y -4 equal to 0 one of the points you get is (0,0). you use this in figuring your saddle point saddle point = 0 confidence assessment: 2
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08:37:50 How did you test each critical point to determine if it is a relative max, relative min or saddle point?
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RESPONSE --> im not sure what the exact critical points are because I'm not sure how to solve 2x + 6y = 0 and 6x +20y - 4 =0 when there are two variables to solve for. but I found the second partial derivative of each and plugged them into d = (fxx)(fyy) - (fxy)^2 confidence assessment: 2
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08:43:44 Query problem 7.5.28 extrema of x^3+y^3 -3x^2+6y^2+3x+12y+7
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RESPONSE --> begin by finding first partial derivatives fx(x,y) = 3x^2 - 6x + 3 fy(x,y) = 3y^2 +12y + 12 set them equal to zero 3x^2 - 6x + 3 = 0 3y^2 +12y + 12 = 0 not sure about others, I know one of the critical points is (0,0). the other two might be (1,1) (-1,-1). confidence assessment: 2
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08:48:00 List the relative extrema and the saddle points of the function and tell which is which, and how you obtained each.
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RESPONSE --> fxx(x,y) = 6x - 6 fyy(x,y) = 6y +12 fxy(x,y) = 0 at (1,1) d = 6 * 6 - 0^2 = 36 fxx(x,y) = 6 relative minimum at (-1,-1) d = 6 * 6 - 0^2 = 36 fxx(x,y) = 6 relative minimum at (0,0) d = 0 * 0 - 0^2 = 0 fxx(x,y) = 0 saddle point confidence assessment: 2
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08:48:14 What are the critical points and what equations did you solve to get them?
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RESPONSE --> previously shown confidence assessment: 0
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08:49:35 How did you test each critical point to determine if it is a relative max, relative min or saddle point?
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RESPONSE --> by using the equation d = (fxx)(fyy) - (fxy)^2 confidence assessment: 2
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08:50:15 At what point(s) did the second-partials test fail?
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RESPONSE --> at (0,0) and this was the saddle point confidence assessment: 1
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