A) If\[f(x)\]is not continuous at\[x=a,\]then it is not differentiable at \[x=a\]
B) If\[f(x)\]is continuous at x = a, then it is differentiable at\[x=a\]
C) If\[f(x)\]and\[g(x)\]are differentiable at\[x=a\], then\[f(x)+g(x)\]is also differentiable at\[x=a\]
D) If a function\[f(x)\]is continuous at\[x=a\], then\[\underset{x\to a}{\mathop{\lim }}\,f(x)\]exists
Correct Answer: B
Solution :
If a function\[f(x)\]is continuous at\[x=a,\]then it may or may not be differentiable at\[x=a\]. \[\therefore \]Option (b) is correct.
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