 Quote by cjaylee
Hey. I am quite confused by continuity and derivatives. Both are finding the limits of a particular function as x approaches a. Then why is it that a graph that is continuous cannot be differentiable? If it is continuous, it means that the limit exists and so, it should be differentiable right?
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What "limit exists"? The limit you look at to determine if f(x) is continuous at x= a, is [itex]\lim_{x\to a} f(x)[/itex] while the limit you look at to determine if f(x) is differentiable at x= a is [itex]\lim_{h\to a} (f(a+h)- f(a))/h[/itex]. It is easy to show that if a function is differentiable at x= a, it must be continuous but the other way is not true.