Exam 14: Partial Derivatives

Select the correct Answer: for each question. -Find equations for the tangent plane and the normal line to the surface with equation at the point

Find the local maximum, and minimum value and saddle points of the function.

The (or humidex, for short) is the perceived air temperature when the actual temperature is T and the relative humidity is h, so we can write The following table of values of I is an excerpt from a table compiled by the National Oceanic and Atmospheric Administration.For what value of T is

Find for the function

Find the dimensions of the rectangular box with largest volume if the total surface area is given as

Find the first partial derivatives of the function.

How many artial derivatives does a function of two variables have?

Find the shortest distance from the point to the plane Select the correct Answer

Find the differential of the function

Suppose that over a certain region of space the electrical potential V is given by Find the rate of change of the potential at in the direction of the vector Select the correct Answer

Select the correct Answer: for each question. -Use implicit differentiation to find

Find the maximum rate of change of at the point In what direction does it occur?

At what point is the following function a local maximum?

Select the correct Answer: for each question. -Find and classify the relative extrema and saddle points of the function

Use partial derivatives to find the implicit derivative

If

Select the correct Answer: for each question. -Find the gradient of the function

Evaluate the limit.

Select the correct Answer: for each question. -Evaluate the limit.

Select the correct Answer: for each question. -Suppose that over a certain region of space the electrical potential V is given by Find the rate of change of the potential at in the direction of the vector