A function f: \mathbb{R} \to \mathbb{R} is defined as f(x)=x^2 for x \geq 0 and f(x)=-x for x

UPSC NDA II 2013 Mathematics Paper

Question : 104 of 120

Marks: +1, -0

A function f:ℝ→ℝ is defined as f(x)=x2 for x≥ 0 and f(x)=−x for x<0.
Consider the following statements in respect of the above function:
1. The function is continuous at x=0.
2. The function is differentiable at x=0.
Which of the above statements is/are correct?

1 only
2 only
Both 1 and 2
Neither 1 nor 2

Validate

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