Calculus 3: Optimization
Given that , identify any critical points, saddle points, and any local extrema.
Find and classify the critical points of .
Given the function on the rectangle D, find the absolute extreme values.
A wire of length 100 centimeters is cut into two pieces; one is bent to form a square, and the other is bent to form an equilateral triangle. Where should the cut be made if (a) the sum of the two areas is to be a minimum; (b) a maximum? (Allow the possibility of no cut.)
Find the local extrema of the function using the second derivative test.
Using the Cobb-Douglas production function , maximize production subject to the constraint .
Using the Cobb-Douglas production function , maximize production subject to the constraint .
Suppose you make TV sets at two different factories, Factory A and Factory B. You produce x TVs at Factory A, y TVs at Factory B, and the cost given by the production of x TVs and y TVs is the function . You need to produce exactly 90 TV sets a month. Determine how many TVs should be produced at each factory to minimize the cost.