‹ Back to the paper
Choose the correct option.
Statement I: f(x) = {x² sin(1/x), if x ≠ 0; 0, if x = 0} is continuous at x = 0 but f'(x) is not…
Statement I: $f(x) = \begin{cases} x^2 \sin\left(\frac{1}{x}\right), & \text{if } x \neq 0 \\ 0, & \text{if } x = 0 \end{cases}$ is continuous at $x = 0$ but $f'(x)$ is not continuous at $x = 0$.
Statement II: The derivative of a continuous function need not be a continuous function.
- (a)Both (I) and (II) are correct and (II) is the correct explanation of (I).
- (b)Both (I) and (II) are correct and (II) is not the correct explanation of (I).
- (c)(I) is correct but (II) is incorrect.
- (d)(II) is correct but (I) is incorrect.
Answer
Answer
Official answer keyCorrect option: (a)
Answer: (a) Both (I) and (II) are correct and (II) is the correct explanation of (I).