Question

6. Find the global maxima and global minima for on the disc r2+y 1. We will divide this into the following steps. (a) (10 points) Please find all critical points of f(r,v) in the region x2 + y2く1 and classify their types. parametrization (b) (10 points) Please find the maximum and minimum of f(r, y) on the boundary z2+y 1 by parametri and minimum of f(r,. y ) on the boundary 2+y2 method. (c) (10 points) Please find the maximum and minimum of f(r,y) on the boundary z2 + 1 by Lagrange multiplier method.

Answer 1

= 2x +y=0; ら=2y+x=0; f (t)-1+costsint f(t) = 1 + _ sin 21 maximum =1+ minimumEl-_ _ 尻=0, 2x +y+2(2x)=0; F, = 0, 2y + x +2(2y) = 0; 2y f(x,x)= 3x22