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Consider the surface a —3xy+4y=z-6x . The normal line to this surface at the point (3,3,3) is
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Not yet (5 points) Consider the surface — +xy*=zZ-—2 . The tangent plane to this surface at (3,2, 14) is
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- (5 points) Let f(x,y) = 4sin(4xy)+ xcos £) +3x“y. Then the gradient of f at (3,0) is
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Not yet (5 points) Let f(x,y) = cos(in(5y*))+ sin(7x*)— ae Then partial derivative of f with respect to x is
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dues: D (5 points) The shortest distance from the point (1,0, —3) to the plane
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(5 points) Let f(x,y) = y7e* ’-5x+y then
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sussicn O (5 points) Find the directions in which the directional derivative of f(x,y) = 1*x?+sin(8*x*y) at (1,0) has the value 8 .
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duesuus 8 (5 points) Let f(x,y,z)=e** ~°”—x*y*z where x = 4 s—3, y=S*, andz=3S+1. Thenat s=0
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auestica 9 Ql) Let f(x,y)=y?+xy*—- 18 x y+ 80x.
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“eee Q2): Consider the level surface g(x,y,z)=x*+ 16 y*+ 16 2? = 16 (this is an ellipsoid). Consider boxes whose center is at the origin and that have a vertex (x,y,z), with x,y,z > 0, on this
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a) (10 pts) Write the volume of the box for f(x,y,Z) with respect to Xx,y,Z. | |
b) (10 pts) Find the critical point(s) for f with respect to the constraint g.
c) (10 pts) Find the maximum volume this box subject to g. Wo rk Problems
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