# Differentiability and continuity relationship tips

### Describe the relationship between differentiability and continuity | Larson Calculus – Calculus 10e

Why is it that all differentiable functions are continuous but not all continuous functions are differentiable? A continuous function is a function whose graph is a single unbroken curve. What does this tell us about the relationship between continuous functions and. In a real 2-Dimensional function f(x) on the X-Y plane, we have the following relations between these concepts: i) f'(x) is continuous if and only f(x) is. In this chapter we shall study limit and continuity of real valued functions defined on certain . The relations in (∗) in the above examples can also be written as.

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