Exam 14: Partial Derivatives

Find three positive numbers whose sum is and whose product is a maximum.

Evaluate the limit.

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 dimensions of a rectangular box of maximum volume such that the sum of the lengths of its 12 edges is

Find the equation of the normal line to the given surface at the specified point.

The wind-chill index I is the perceived temperature when the actual temperature is T and the wind speed is v so we can write The following table of values is an excerpt from a table compiled by the National Atmospheric and Oceanic Administration.Use the table to find a linear approximation to the wind chill index function when T is near and v is near 30 kmh.

Find the gradient of

Select the correct Answer: for each question. -Let

Find the equation of the normal line to the given surface at the specified point.

Use implicit differentiation to find

Evaluate the limit.

Find the indicated partial derivative.

The radius of a right circular cone is increasing at a rate of 5 in/s while its height is decreasing at a rate of 3.6 in/s.At what rate is the volume of the cone changing when the radius is and the height is ?

Determine the largest set on which the function is continuous.

Find the gradient of the function

Determine where the function is continuous.

Describe the level survaces of the function

Use the Chain Rule to find

Find equations for the tangent plane and the normal line to the surface with equation t the point

Use the Chain Rule to find