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Statement I: is continuous at but is not continuous at . Statement II: The derivative of a…

Mathematics20251 markMCQ
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

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Continuity, Differentiability and Differentiation

From ISC 2025 Practice Mathematics, question 32.