Differentiability and Continuity
continuity and differentiability of Class 12
Differentiability and Continuity
(a) If f′(a) and f′(a) exist finitely both may or may not be equal then f(x) is continuous at x = a.
(b) If f(x) is differentiable at every point of its domain, then it must be continuous in that domain.
(c) The converse of the above result is not true i.e., if f(x) is continuous at x = a then it may or may not be differentiable at x = a.
(d) If f(x) is differentiable then its graph must be smooth i.e. there should be no break or corner.
- Continuity of A Function
- Discontinuity of A Function
- Derivatives
- Differentiability and Continuity
- Some Standard Differentials
- Derivative of Parametric and Logarithmic Functions
- Some Standard Substitutions
- Exercise 1
- Exercise 2
- Exercise 3
- Exercise 4
- Exercise 5
- Exercise 6
- Exercise 7
- Exercise 8
- Exercise 9
- Exercise 10
