Question

If a function is differentiable, then it is continuous? correct

Answer 1

http://en.wikipedia.org/wiki/Differentiable#Differentiability_classes
This function is differential but not continuous lol

Answer 2

I think you read it incorrectly. They made it a piecewise and fill in the pt of discount with a point. I believe this is a theorem. You can assume a function is continuous if you can take the derivative of it. I know it is not the other way around "ie if a function is continuous then it is differential".

Answer 3

lol ok but the wikipedia provided a counterexample...

Answer 4

continuously differentiable
I copied and paste this from the link you provided......Sorry but this is not a counterexample.

Answer 5

@hartnn

Answer 6

"If f is differentiable at a point x0, then f must also be continuous at x0. In particular, any differentiable function must be continuous at every point in its domain. The converse does not hold: a continuous function need not be differentiable."

-Wikipedia article sited above

Answer 7

is f(x)=1/x continuous everywhere?
is it differentiable?

Answer 8

wow that is a brilliant example i lyk dat

Answer 9

ok thanks then I was correct about the hypothesis. I knew the converse was not true since I knew some counterexamples (ie functions with corners for example absolute value functions at their vertex)

Answer 10

If I am looking at a piecewise that I know is continuous. I would need to take the derivative of each function given to determine if they have the same limit correct?

Answer 11

I think that's right; it's the only way I can think of :P

Answer 12

Thanks just double checking my thinking for an upcoming final exam.

Answer 13

Always a good idea ;)