Question 3

a. Prove that the function $f(x,y) = \sqrt{|xy|}$ is not differentiable at origin. Do its partial derivatives exist at origin? Justify. (3 marks)

b. Show that the function $f(x,y) = 2x^4 - 3x^2y + y^2$ has neither maximum nor a minimum at $(0,0)$. (2 marks)