Question

Find the minimum value of the function f(x, y) = x^2 + y^2 +199 over the real domain.

(a) 12

(b) 13

(c) 0

(d) 199

This question was posed to me during a job interview.

This key question is from Maxima and Minima of Two Variables topic in chapter Maxima and Minima of Engineering Mathematics

Answer 1

Correct choice is (d) 199

For explanation: Find

fx = 2x

fy = 2y

The critical point is

x=0

y=0

(0,0) is the critical point

Put it back into the function we get

z = 0 + 0 + 199 = 199 is the required minimum value.