Mathematics · Real Analysis
For a positive real number a, √a denotes the positive square root of a. Consider the function f : ℝ2 → ℝ defined by: f(x, y) = x|x|√(x2 + y2) if x ≠ 0, and f(x, y) = 0 if x = 0. Which of the following statements is FALSE regarding the function f?
Verified Solution4 OptionsUpdated: October 2026👁️1 View
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- 1f is not differentiable at (0, 0).
- 2f is differentiable at (0, 0).✓
- 3The partial derivatives ∂f/∂x and ∂f/∂y exist at (0, 0).
- 4f is continuous at (0, 0).
Correct answer
f is differentiable at (0, 0).
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