Question

Stationary point is a point where, function f(x,y) have?

(a) ^∂f⁄∂x = 0

(b) ^∂f⁄∂y = 0

(c) ^∂f⁄∂x = 0 & ^∂f⁄∂y = 0

(d) ^∂f⁄∂x < 0 and ^∂f⁄∂y > 0

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

My doubt stems from Maxima and Minima of Two Variables topic in section Maxima and Minima of Engineering Mathematics

Answer 1

Correct option is (c) ^∂f⁄∂x = 0 & ^∂f⁄∂y = 0

The explanation: Point where function f(x,y) either have maximum or minimum value is called saddle point. i.e, ^∂f⁄∂x = 0 & ^∂f⁄∂y = 0.