Home › CBSE 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.
Related questions
Two things this chain introduces beside continuity are differentiability and:Composites of continuous functions, by Theorem 2, are:A function that fails the limit test at a point is:To differentiate an implicit relation you use the:The function f(x) = |x| at x = 0 is continuous but not:For f(x) = 2x + 3 at x = 1, the limit and f(1) are both:An alternative to repeated product rule for many factors is:The chain rule can be extended to composites of: