Mathematics I (Calculus) - Old Questions

15. Find the extreme value of f(x, y) = y² − x² .

Given

f(x, y) = y²-x²

Then

Also

For critical point,

This gives, x=0, y=0.

At point (0, 0)

Here, at point (0, 0)

and

The function has a saddle point at the (0, 0) and no local extreme values.