Differentiability of a Function

# Differentiability of a Function Video Lecture | Mathematics (Maths) Class 12 - JEE

## Mathematics (Maths) Class 12

204 videos|288 docs|139 tests

## FAQs on Differentiability of a Function Video Lecture - Mathematics (Maths) Class 12 - JEE

 1. What does it mean for a function to be differentiable?
Ans. A function is said to be differentiable at a point if the derivative of the function exists at that point. In simpler terms, it means that the function has a well-defined instantaneous rate of change at that specific point.
 2. How can I determine if a function is differentiable at a given point?
Ans. To determine if a function is differentiable at a given point, you need to check if the left-hand derivative and the right-hand derivative exist and are equal at that point. If they are equal, then the function is differentiable at that point. However, if they are not equal, or if one or both derivatives do not exist, then the function is not differentiable at that point.
 3. Can a function be differentiable everywhere except at a single point?
Ans. No, if a function is not differentiable at a single point, it is not differentiable in the entire domain. Differentiability requires the existence of derivatives at each point in the function's domain. If there is a single point where the derivative does not exist, then the function is not differentiable anywhere.
 4. Is every continuous function differentiable?
Ans. No, not every continuous function is differentiable. Although all differentiable functions are continuous, the converse is not true. There are continuous functions that are not differentiable at certain points, such as functions with sharp corners or discontinuities in their graphs.
 5. Can a function be differentiable but not continuous?
Ans. No, a function cannot be differentiable at a point if it is not continuous at that point. Differentiability implies continuity. If a function is not continuous at a certain point, it cannot have a derivative at that point, and therefore, it is not differentiable at that point.

## Mathematics (Maths) Class 12

204 videos|288 docs|139 tests

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