Exam 13: Section 3: Functions of Several Variables

For , evaluate at the point .

Find the partial derivative for the function .

For , evaluate at the point .

Find the partial derivative for the function .

Suppose the temperature at any point in a steel plate is where x and y are measured in meters. At the point find the rate of change of the temperature with respect to the distance moved along the plate in the direction of the x-axis. Round your answer to one decimal place.

Suppose a pharmaceutical corporation has two plants that produce the same over-the-counter medicine. If and are the numbers of units produced at plant 1 and plant 2, respectively, then the total revenue for the product is given by . When and find the marginal revenue for plant 1.

Find the second partial derivative for the function with respect to x.

Find the partial derivative for the function .

For find all values of x and y such that and simultaneously.

Find the first partial derivative for the function with respect to z.

For , evaluate at the point .

Suppose the utility function is a measure of the utility (or satisfaction) derived by a person from the consumption of two products x and y. Determine the marginal utility of product if the utility function is .

For , find all values of x and y such that and simultaneously.

Find the partial derivative for the function .

Find the partial derivative for the function .

Suppose a company manufactures two types of wood-burning stoves: a freestanding model and a fireplace-insert model. The cost function for producing x freestanding and y fireplace-insert stoves is . Find the marginal costs when and . Round your answer to the nearest integer.

Find the partial derivative for the function .

Find the partial derivative for the function .

For , evaluate at the point .

For find all values of x and y such that and simultaneously.