Calculus/continous

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Expert: - 5/31/2008


Question
Dear Sir,
I am megahana and undergraduate student. I am not understanding that,
1) what is exact difference between continuous and differentiability? 2)
some times, some functions are continuous but not differentiable. how?
I am fully confused in this part. please explain with a suitable
example.
Thanking you,
yours faithfully,
Meghna

Answer
1. Continuous means a curve can be drawn fron left to right to represent the function without lifting the pencil from the graph paper.  Differentiable means the line has no corners.  An example of a curve that is continuous but not every differentiable is f(x)=|x|.  It is differentiable at every point but 0.

Another is f(x) = |sin(x)|.  This is coninuous, but not differentiable at n*pi, where n is any even number.

If you let f(x)=|sin(x/m)| for larger and larger m, there are more points at which the function is not differentiable, but I don't see how a function can be continuous without being differentiable at any point.  Let me know if you find one.

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