View Single Post
HallsofIvy
HallsofIvy is offline
#4
Oct3-09, 05:39 PM
Math
Emeritus
Sci Advisor
Thanks
PF Gold
P: 38,881

Difference between Continuity and Derivatives.


Quote Quote by cjaylee View Post
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?
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.