Exam 11: Extension G: Partial Derivatives

Find the critical points of the function.

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

Find the absolute extrema of the function on the closed triangular region with vertices , and

Find the shortest distance from the point to the plane

Find and classify the relative extrema and saddle points of the function for and

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

Find the absolute minimum value of the function on the set D.D is the region bounded by the parabola and the line

Suppose (1,1)is a critical point of a function f with continuous second derivatives. In the case of , , what can you say about f ?

Find and classify the relative extrema and saddle points of the function

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

A cardboard box without a lid is to have a volume of cm Find the dimensions that minimize the amount of cardboard used.

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

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

Find the points on the surface that are closest to the origin.