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Magazine Problem 358
For the following exercises, use the method of Lagrange multipliers to find the maximum and minimum values of the function subject to the given constraints. \(f(x, y)=x^{2} y ; x^{2}+2 y^{2}=6\)
Problem 359
For the following exercises, use the method of Lagrange multipliers to find the maximum and minimum values of the function subject to the given constraints. \(f(x, y, z)=x y z, x^{2}+2 y^{2}+3 z^{2}=6\)
Problem 360
For the following exercises, use the method of Lagrange multipliers to find the maximum and minimum values of the function subject to the given constraints. \(f(x, y)=x y ; 4 x^{2}+8 y^{2}=16\)
Problem 361
For the following exercises, use the method of Lagrange multipliers to find the maximum and minimum values of the function subject to the given constraints. \(f(x, y)=4 x^{3}+y^{2} ; 2 x^{2}+y^{2}=1\)
Problem 362
For the following exercises, use the method of Lagrange multipliers to find the maximum and minimum values of the function subject to the given constraints. \(f(x, y, z)=x^{2}+y^{2}+z^{2}, x^{4}+y^{4}+z^{4}=1\)
Problem 363
For the following exercises, use the method of Lagrange multipliers to find the maximum and minimum values of the function subject to the given constraints. \(f(x, y, z)=y z+x y, x y=1, y^{2}+z^{2}=1\)
Problem 364
For the following exercises, use the method of Lagrange multipliers to find the maximum and minimum values of the function subject to the given constraints. \(f(x, y)=x^{2}+y^{2},(x-1)^{2}+4 y^{2}=4\)
Problem 365
For the following exercises, use the method of Lagrange multipliers to find the maximum and minimum values of the function subject to the given constraints. \(f(x, y)=4 x y, \frac{x^{2}}{9}+\frac{y^{2}}{16}=1\)
Problem 366
For the following exercises, use the method of Lagrange multipliers to find the maximum and minimum values of the function subject to the given constraints. \(f(x, y, z)=x+y+z, \frac{1}{x}+\frac{1}{y}+\frac{1}{z}=1\)
Problem 367
For the following exercises, use the method of Lagrange multipliers to find the maximum and minimum values of the function subject to the given constraints. \(f(x, y, z)=x+3 y-z, x^{2}+y^{2}+z^{2}=4\)
