Q50Multiple correct2 Marks3 Sep 2023

Let f(x, y) = { xy/(x^2 + y^2) if $(x, y)$ != $(0, 0)$, and 0 otherwise. Then which of the following statement(s) is/are true?

A

The partial derivatives for f exist everywhere but directional derivatives neednot exist at the origin.

B

All directional derivatives at the origin exist for the function f.

C

At $(0, 0)$, the directional derivative of f exists in the direction of x-axis.

D

The partial derivatives for f do not exist at the origin.