Home › UP Board Class 12 › mathematics › Continuity and Differentiability › A function differentiable at $x = a$ is always:
A function differentiable at $x = a$ is always:
ADiscontinuous at $a$, never the case for school chart usage
BEqual to zero at $a$, since derivative gives slope on chart
CContinuous at $a$, since differentiability implies continuity
DBounded on a neighbourhood of $a$ with no limit value at $a$
Answer & Solution
Correct answer: C. Continuous at $a$, since differentiability implies continuity
If $f'(a)$ exists, $f$ is continuous at $a$. Converse is false.
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