The continuity is always referred to as a function that is considered the features of the graphical presentation. At the same time, the differentiability of a function is the functions whose derivatives do exist at the domain of each point.
Conditions of Continuity
The function is only considered the continuous function when it only performs the three main things.
- When f(a) is defined.
- When the limit of the function exists.
- When limit f(x) = f(a)
Guarantees of continuity and differentiability
- When we talk about Continuity and Differentiability, continuity does not guarantee differentiability.
- Whereas when we talk about Differentiability, the differential function is always considered the continuous function for every domain point.
- It is considered that the differential functions are always atypical compared to the continuous functions.
Limit concept of continuity
- The limit is the fixed value for approaching a specific number.
- Example: f(x) = 3x
- Limit of approaching f(x) = 3 from x to 2 is 6.
Relationship between continuity & differentiability
The relationship between differentiability & continuity is different. The differentiability term is considered as the continuous function.
But the continuous function is not considered as the differentiable function. Both these continuity & differentiability terms are very different from each other.