Questions from General Calculus

Q: Interpret ∂f/∂y (2, 3) as a

Interpret ∂f/∂y (2, 3) as a rate of change.

Q: Give an example of a Cobb–Douglas production function. What

Give an example of a Cobb–Douglas production function. What is the marginal productivity of labor? Of capital?

Q: Explain how to find possible relative extreme points for a function of

Explain how to find possible relative extreme points for a function of several variables.

Q: State the second-derivative test for functions of two variables.

State the second-derivative test for functions of two variables.

Q: Outline how the method of Lagrange multipliers is used to solve an

Outline how the method of Lagrange multipliers is used to solve an optimization problem.

Q: What is the least-squares line approximation to a set of

What is the least-squares line approximation to a set of data points? How is the line determined?

Q: Find a function f (x, y) that has the

Find a function f (x, y) that has the line y = 3x - 4 as a level curve.

Q: Give a geometric interpretation for ∫R∫ f (x,

Give a geometric interpretation for ∫R∫ f (x, y) dx dy, where f (x, y) ≥ 0.

Q: Give a formula for evaluating a double integral in terms of an

Give a formula for evaluating a double integral in terms of an iterated integral.

Q: Give an example of a level curve of a function of two

Give an example of a level curve of a function of two variables.