Which of the following statements is true?

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(D) The correct statement is $(d)$. By the fundamental theorem of calculus,if a function $f(x)$ is differentiable at a point $x = c$,then it must be c

Vedclass · Accepted Answer

$A$ differentiable function is continuous.

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(D) The correct statement is $(d)$. By the fundamental theorem of calculus,if a function $f(x)$ is differentiable at a point $x = c$,then it must be continuous at that point $x = c$. However,the converse is not necessarily true; a continuous function may not be differentiable (e.g.,$f(x) = |x|$ at $x = 0$). Therefore,$(d)$ is the only universally true statement among the given options.

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