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Magazine Problem 324
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. $$f(x, y)=x^{3}+y^{3}-300 x-75 y-3$$
Problem 325
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. $$f(x, y)=9-x^{4} y^{4}$$
Problem 326
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. $$f(x, y)=7 x^{2} y+9 x y^{2}$$
Problem 327
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. $$f(x, y)=3 x^{2}-2 x y+y^{2}-8 y$$
Problem 328
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. $$f(x, y)=3 x^{2}+2 x y+y^{2}$$
Problem 329
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. $$f(x, y)=y^{2}+x y+3 y+2 x+3$$
Problem 330
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. $$f(x, y)=x^{2}+x y+y^{2}-3 x$$
Problem 331
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. $$f(x, y)=x^{2}+2 y^{2}-x^{2} y$$
Problem 332
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. $$f(x, y)=x^{2}+y-e^{y}$$
Problem 333
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. $$f(x, y)=e^{-\left(x^{2}+y^{2}+2 x\right)}$$
