Kind of off-topic but if infinitely differentiable implies differentiable which implies continuous that implies defined is there something stronger than infinitely differentiable?

3 A function is differentiable (has a derivative) at point x if the following limit exists: $$ \lim_ {h\to 0} \frac {f (x+h)-f (x)} {h} $$ The first definition is equivalent to this one (because for this limit to …

Oct 26, 2010 · So it would appear that if functions are not differentiable, it can only happen at a finite number of points. In real analysis, this concept of being differentiable everywhere except …

In fact you can show that a differentiable function on an open interval (not necessarily a bounded interval) is Lipschitz continuous if and only if it has a bounded derivative. This is because any …

Why are all differentiable functions continuous, but not all continuous functions differentiable? For the same reason that all cats are animals, but not all animals are cats. Differentiability also …

A function is "differentiable" if it has a derivative. A function is "continuous" if it has no sudden jumps in it. Until today, I thought these were merely two equivalent definitions of the same c...

Jul 21, 2020 · Is the derivative of a differentiable function always continuous? My intuition goes like this: If we imagine derivative as function which describes slopes of (special) tangent lines …

Jan 24, 2015 · A function is said to be differentiable at a point if the limit which defines the derivate exists at that point. However, the function you get as an expression for the derivative …

May 16, 2018 · An example of graph which is continuous but not differentiable is given below . Can we identify the non differentiable functions from graph plot as we did earlier in continuity?

Mar 3, 2024 · The way I think about differentiability is like this: "Can a function be differentiated at every point?" But that doesn’t really help me, I have been looking for a specific formula I can …