Yes there is. is continuous for all x, but is not differentiable at , where is any real number.
my question can we derive any equation for example
this equation is the positive x-axis and the positive y-axis
I do not want to make it more complicated
in other word if we have a question that asks us to find should we first look if this is a curve or dose it have points on it ??
is there any continuous function that is not differentiable at all point of the domain ?
Thanks
For this particular problem, use "implicit differentiation"
Do you mean something like ?this equation is the positive x-axis and the positive y-axis
I do not want to make it more complicated
in other word if we have a question that asks us to find should we first look if this is a curve or dose it have points on it ??
Well, if the problem asks you to find dy/dx, it would be a very poor question if there were no points!
As sambit said, y= |x- a|, for any real number a, is continuous for all x but not differentiable at x= a. There even exist functions that are continuous for all x but not differentiable for any x but they are difficult to write.is there any continuous function that is not differentiable at all point of the domain ?
Thanks
"is there any continuous function that is not differentiable at all point of the domain ?" If my math history is correct, I think it was Weierstrass who first derived a continuous function that's not differentiable at any of its points!
The equation you offered also works at the origin just to remind you. And it's always good to test out the equation looking for points associated with the maxima/minima of the curve and other properties to help distinguish it