Question

For function f(x, y) = sin^-1(x^2 + y^2) critical points are found. Now a new graph g(x, y) is formed by coupling graphs f(x, y) and f(x, y) = – sin^-1(x^2 + y^2). What are the critical points of g(x, y).

(a) (0,0)

(b) There are infinite such points

(c) Only positive (x, y) are critical points

(d) (90,-90)

The question was posed to me by my school principal while I was bunking the class.

The query is from Maxima and Minima of Two Variables topic in chapter Maxima and Minima of Engineering Mathematics

Answer 1

The correct option is (b) There are infinite such points

To explain I would say: The function takes constant values along a circle(observe the function)

But it is composed of arc sine function. Hence, we will have critical points at equal intervals

Hence, there are infinite such points.