Question

2. (4 pts) Let f(x,y) =x2+y2. Mark the locations where f attains its minimum and maximum on the triangle constraint shown in Figure 1. Clearly indicate “minimum” or “maximum” at each location.

2 0 X FIGURE 1. Figure for Problem 2. 2. (4 pts) Let f(x, y) = x2 + y². Mark the locations where f attains its minimum and maximum on the triangle constraint shown in Figure 1. Clearly indicate "minimum" or "maximum" at each location.

Answer 1

ANSWER :

Since given figure

X -l Monimum point

Now given function

Let

  

Z= x2 + y2........(2)

Therefore equation (2) is parabolic in (3D)

$Here \, \, z\geq 0,\, \,\forall \, \, x, y\, \epsilon \, \, R$

Now,

is maximum where projection of parabolic have maximum radius  

조 T

I. e., when z is maximum .

I. e., the radius of triangle

$x^{2}+y^{2}=z$ (radius) is maximum.

And similarly function $f(x,y)=x^{2}+y^{2}$ is maximum where the projection of parabolic maximum radius  

SS ( 2 )