Question У. 5. A contour map for the function f(x,y) = 4 + x3 + y3 – 3xy is shown. Use the contour map to predict the location of the critical points of f(x,y) and whether f(x, y) has a saddle point or local maximum or minimum at each critical point. Then use the Second Derivatives Test to confirm your predictions. 3.2 3.7 4 4.2 X 3.7 3.2 6 0
X4O327 The Asker · Advanced Mathematics
Transcribed Image Text: У. 5. A contour map for the function f(x,y) = 4 + x3 + y3 – 3xy is shown. Use the contour map to predict the location of the critical points of f(x,y) and whether f(x, y) has a saddle point or local maximum or minimum at each critical point. Then use the Second Derivatives Test to confirm your predictions. 3.2 3.7 4 4.2 X 3.7 3.2 6 0
More Transcribed Image Text: У. 5. A contour map for the function f(x,y) = 4 + x3 + y3 – 3xy is shown. Use the contour map to predict the location of the critical points of f(x,y) and whether f(x, y) has a saddle point or local maximum or minimum at each critical point. Then use the Second Derivatives Test to confirm your predictions. 3.2 3.7 4 4.2 X 3.7 3.2 6 0
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AnswerPage-1f(x,y)=4+x^(3)+y^(3)-3xy.For critical points:(del f)/(del x)=0quad f(del f)/(del y)=0{:[f_(x)=3x^(2)-3y=0quad=>quad3(x^(2)-y)=0],[x^(2)=y quad-" (1) "],[f_(y)=3y^(2)-3x=0=>3(y^(2)-x)=0],[y^(2)-x=0quady^(2)=x.]:}{:[=>x^(4)=x],[=>x^(4)-x=0=>x(x^(3)-1)=0],[=>x(x-1)(x^(2)+x+1)=0]:}by (1) f(2){:[", ":.x=0" or "x-1=0=>x=1],[=>x=0","1","quad y=x^(2)quad y(0)=0],[y(1)=1]:}HenceGitical point are (0,0),(0,1),(1,0),(1,4)##for maxima, Minima & saddle Point:(j) rt-s^(2) > 0quad (maxima. & minima)if r < 0 marima.if r > 0quad minima(ii) quad rt-s^(2)=0 saddl ... See the full answer