Consider the following statements.(a) If a fu | vedclass

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(B) Statement $(a)$ is incorrect because if a function is differentiable at a point, it must be continuous at that point.Statement $(b)$ is correct be

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$(b)$ and $(c)$

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(B) Statement $(a)$ is incorrect because if a function is differentiable at a point, it must be continuous at that point.Statement $(b)$ is correct because differentiability implies continuity; therefore, the contrapositive (not continuous implies not differentiable) is also true.Statement $(c)$ is correct because $f(x) = |x|$ is continuous for all $x \in R$ but is not differentiable at $x = 0$.Statement $(d)$ is incorrect because $f(x) = x - [x]$ is the fractional part function, which is discontinuous at all integers, including $x = 1$. Since it is discontinuous at $x = 1$, it is not differentiable at $x = 1$.Thus, statements $(b)$ and $(c)$ are correct.

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