Questions from General Calculus

Q: Find all points (x, y) where f (x

Find all points (x, y) where f (x, y) has a possible relative maximum or minimum. f (x, y) = x3 + 3x2 + 3y2 - 6y + 7

Q: Find all points (x, y) where f (x

Find all points (x, y) where f (x, y) has a possible relative maximum or minimum. f (x, y) = ½ x2 + 4xy + y3 + 8y2 + 3x + 2

Q: Find all points (x, y) where f (x

Find all points (x, y) where f (x, y) has a possible relative maximum or minimum. Then, use the second-derivative test to determine, if possible, the nature of f (x, y) at each of these points. If the...

Q: Find all points (x, y) where f (x

Find all points (x, y) where f (x, y) has a possible relative maximum or minimum. Then, use the second-derivative test to determine, if possible, the nature of f (x, y) at each of these points. If the...

Q: Find all points (x, y) where f (x

Find all points (x, y) where f (x, y) has a possible relative maximum or minimum. Then, use the second-derivative test to determine, if possible, the nature of f (x, y) at each of these points. If the...

Q: Find the values of x, y, z at which f

Find the values of x, y, z at which f (x, y, z) = x2 + 4y2 + 5z2 - 6x + 8y + 3 assumes its minimum value.

Q: Use the method of Lagrange multipliers to: Maximize 3x2 +

Use the method of Lagrange multipliers to: Maximize 3x2 + 2xy - y2, subject to the constraint 5 - 2x - y = 0.

Q: Use the method of Lagrange multipliers to: Find the values

Use the method of Lagrange multipliers to: Find the values of x, y that minimize -x2 - 3xy – ½ y2 + y + 10, subject to the constraint 10 - x - y = 0.

Q: Use the method of Lagrange multipliers to: Find the values

Use the method of Lagrange multipliers to: Find the values of x, y, z that minimize 3x2 + 2y2 + z2 + 4x + y + 3z, subject to the constraint 4 - x - y - z = 0.

Q: Find the dimensions of a rectangular box of volume 1000 cubic inches

Find the dimensions of a rectangular box of volume 1000 cubic inches for which the sum of the dimensions is minimized.