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wat is the relation between continuity and differentiablity?????
f(x) is differentiable (finitely) at x = a => f(x) is continuous at x = a f(x) is not continuous at x = a => f(x)is not differentiable (finitely) at x = a # While examining the continuity and differentiability of a function f(x) at a point x = a,if you start with differentiability and find that f(x) is differentiable then u can conclude that the function is also continuous. # But if u find that the f(x) is not differentiable at x = a, you will also have to check the continuity separately. # Instead ,if you start with continuity and find that the function is not continuous then you can conclude that the function is also non differentiable . # But if u find f(x) is continuous,you will also have to check the differentiability separately.
The following graphs illustrate the relationship between continuity and differentiability.
This graph of the left is continuous at every real number but this graph is not differentiable at x = 1. The graph of the right is not continuous at x = 1 so it certainty is not differentiable there.
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