Question

Consider the f(x, y) = x^2 + y^2 – a. For what values of a do we have critical points for the function.

(a) independent of a

(b) for any real number except zero

(c) a ∊ (0, +∞)

(d) a ∊ (-1, 1)

This question was posed to me by my college professor while I was bunking the class.

My question is from Maxima and Minima of Two Variables topic in portion Maxima and Minima of Engineering Mathematics

Answer 1

The correct option is (a) independent of a

To elaborate: Consider

fx = 2x

and

fy = 2y

There is no a here. Thus, independent of a.