Consider the function f : R^2 to R defined by f(x, y) = begincases x^3 + y^3/sqrtx^2 + 2y^2, & (x, y) ne 0 0, & (x, y) = 0 endcases. Which of the following statements is/are correct?

Q49Section ST (Statistics (Q11–Q65))49 of 65

Cubic over a norm: differentiability

Consider the function $f : \mathbb{R}^2 \to \mathbb{R}$ defined by $f(x, y) = \begin{cases} \dfrac{x^3 + y^3}{\sqrt{x^2 + 2y^2}}, & (x, y) \ne 0 \ 0, & (x, y) = 0 \end{cases}$ . Which of the following statements is/are correct?

Multiple select: one or more options are correct. Select all of them, then submit — marks need the exact set.

Select every correct option, then submit.

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