# How do you normally check if functions are differentiable?

1. Jul 2, 2007

### muskan

plz help me to find out the solution of this question its very simple but i am confused.the question is

"CAN WE CHECK A FUNCTION WHICH IS NOT DIFFERENTABLE EXCATLY AT TWO POINT>IF YES THEN HOW WE CHECK IT"
can i use sin or cos function,or is the graph is straight or not:surprised

2. Jul 2, 2007

### ZioX

How do you normally check if functions are differentiable?

3. Jul 2, 2007

### chaoseverlasting

Use the fundamental definition of a derivative to find the left hand derivative (LHD) and the right hand derivative (RHD). If LHD=RHD, then function is differentiable, if they arent equal, then its not.

4. Jul 2, 2007

### HallsofIvy

Staff Emeritus
What do you mean by "check" a function? And, you would use whatever function you are given, of course, not "sine or cosine". Clearly I am misunderstanding.

5. Jul 3, 2007

### muskan

we have to draw a graph of such function WHICH IS NOT DIFFERENTABLE EXCATLY AT TWO POINT ,no function is given,that is we have to find out a function wich is not differentable excatly two points,and except these two points the function is diffable

6. Jul 3, 2007

### Integral

Staff Emeritus
Be reminded that we do not provide answers here. We provide guidance. Now, Show us some of your thoughts about this. Do you know any functions which are not differentiable at a point? What can you tell us about functions which are not differentiable at a point?

7. Jul 3, 2007

### ZioX

I am confused. Do you want to find a function that is differentiable at only two points? Or do you want to find a function that is not differentiable at two points?

The latter is fairly easy. Remember that the function f(x)=|x| is not diff'ble at x=0. Why not? So can you play with this function to create two points where it is not differentiable?

The former is a bit more complicated. The most natural way would be to map the irrationals and rationals differently in such a way that they coincide at two particular points.

8. Jul 3, 2007

### muskan

i know that this is not for hme work questions but i needed some little help
there are many functions wich are not diffable such
X3 sin 1/x the function will not be difrreable if left hand limit and write hand limt are not same

9. Jul 3, 2007

### CompuChip

Remember that there is a difference between continuous and differentiable.
Continuous means, you can draw the graph without taking your pen off the paper. For example, a sawtooth graph is continuous.
Differentiable means the function is smooth, that it "bends" insteads of "breaks". Think about the difference.

Though differentiability implies continuity, the converse is not true. So you don't really need an example like $\sin 1/x$ -- it's much easier to find an ordinary, continuous function but which is not differentiable. Also see ZioX's comment above.

10. Jul 3, 2007

### muskan

thanks for ur infomation.ZioX's give an exapmle which is not differble at 0.this is one point not two points,we havw to find such fuction wich is not diffable at two points but others points it is differable

11. Jul 3, 2007

### muskan

okkkkk thanks to all i got an answer .

12. Jul 3, 2007

### CompuChip

Well?
Tell us, we're curious :)