Question

f(x, y)=\(10y(10y-1)+(\frac{x^3sin(x^2)tan(x^3)}{(x-1)^3})-100y^2\). Find the critical points

(a) (0,0)

(b) (1,1)

(c) (2,22)

(d) None exist

The question was posed to me in an interview.

Origin of the question is Maxima and Minima of Two Variables in section Maxima and Minima of Engineering Mathematics

Answer 1

Right choice is (d) None exist

Explanation: Rewriting the function

f(x, y)=\((\frac{x^3sin(x^2)tan(x^3)}{(x-1)^3})-10y\)

Differentiating with respect to y we get

fy = -10

-10 ≠ 0

There exist no critical point.