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Magazine Problem 334
For the following exercises, use the second derivative test to identify any critical points and determine whether each critical point is a maximum, minimum, saddle point, or none of these. $$f(x, y)=x^{2}+x y+y^{2}-x-y+1$$
Problem 335
For the following exercises, use the second derivative test to identify any critical points and determine whether each critical point is a maximum, minimum, saddle point, or none of these. $$f(x, y)=x^{2}+10 x y+y^{2}$$
Problem 336
For the following exercises, use the second derivative test to identify any critical points and determine whether each critical point is a maximum, minimum, saddle point, or none of these. $$f(x, y)=-x^{2}-5 y^{2}+10 x-30 y-62$$
Problem 337
For the following exercises, use the second derivative test to identify any critical points and determine whether each critical point is a maximum, minimum, saddle point, or none of these. $$f(x, y)=120 x+120 y-x y-x^{2}-y^{2}$$
Problem 338
For the following exercises, use the second derivative test to identify any critical points and determine whether each critical point is a maximum, minimum, saddle point, or none of these. $$f(x, y)=2 x^{2}+2 x y+y^{2}+2 x-3$$
Problem 339
For the following exercises, use the second derivative test to identify any critical points and determine whether each critical point is a maximum, minimum, saddle point, or none of these. $$f(x, y)=x^{2}+x-3 x y+y^{3}-5$$
Problem 340
For the following exercises, use the second derivative test to identify any critical points and determine whether each critical point is a maximum, minimum, saddle point, or none of these. $$f(x, y)=2 x y e^{-x^{2}-y^{2}}$$
Problem 341
For the following exercises, determine the extreme values and the saddle points. Use a CAS to graph the function. $$[T]f(x, y)=y e^{x}-e^{y}$$
Problem 342
For the following exercises, determine the extreme values and the saddle points. Use a CAS to graph the function. $$[T]f(x, y)=x \sin (y)$$
Problem 343
For the following exercises, determine the extreme values and the saddle points. Use a CAS to graph the function. $$f(x, y)=\sin (x) \sin (y), x \in(0,2 \pi), y \in(0,2 \pi)$$
