Consider the following statements: I. The function is increasing in the interval (-\infty, \infty). II. The function is differentiable at x=0. Which of the statements given above is/are correct?

Explanation

The function can be written as f(x) = x^2 for x \geq 0 and -x^2 for x \lt 0. Its derivative is f'(x) = 2x for x \geq 0 and -2x for x \lt 0, meaning f'(x) = 2|x|. Since f'(x) \geq 0 for all real x, the function is strictly increasing on (-\infty, \infty). Also, the left and right hand derivatives at x=0 are both 0, making it differentiable at x=0. Thus, both statements are correct.

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