Find the maximum and minimum values of the function subject to the constraint .

Question

Find the maximum and minimum values of the function  subject to the constraint  .

Quizplus · Accepted Answer

By Lagrange Multipliers, we have:
11eb12b0_a926_0fbd_b394_db0e4ee07404_TB7866_12x = 2λcos(2x)
11eb12b0_a926_0fbd_b394_db0e4ee07404_TB7866_12y = 3λcos(3y)

Hence, either cos(2x) = 0 or cos(3y) = 0. These give the maximum and minimum values of the function:

Max: f(pi/4, 0) = sqrt(2)
Min: f(0, pi/6) = -sqrt(3) / 2

Therefore, the answer is C.

Find the Maximum and Minimum Values of the Function