You are Here: Home >< Maths

# Analysis questions watch

1. This may sound like a stupid question, but if a function has a second derivative, does that mean it has a first derivative?

Also, if a function f : (0,1) --> R is 2 times differentiable, does that mean f : (x,x+h) --> R is 2 times differentiable? (x and x+h are in the interval (0,1)
2. (Original post by asdfyolo)

Also, if a function f : (0,1) --> R is 2 times differentiable, does that mean f : (x,x+h) --> R is 2 times differentiable? (x and x+h are in the interval (0,1)
Are you saying that ?
3. (Original post by Zacken)
Are you saying that ?
yes
4. (Original post by asdfyolo)
yes
I can't see why that wouldn't be two times differentiable, but I'd gladly be corrected by someone else.
5. (Original post by Zacken)
I can't see why that wouldn't be two times differentiable, but I'd gladly be corrected by someone else.
Thanks. How would you go about proving that the limit of (f(x+h)+f(x-h)-2f(x))/h^2 as h tends to zero is the second derivative, using taylor's theorem?
6. (Original post by asdfyolo)
Thanks. How would you go about proving that the limit of (f(x+h)+f(x-h)-2f(x))/h^2 as h tends to zero is the second derivative, using taylor's theorem?
If you're using Taylor's Theorem, this does however assume that the function is twice differentiable at .
Write: .
Expand similarly and the result follows.

### Related university courses

TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: March 17, 2016
Today on TSR

### 1,055

students online now

Exam discussions

Poll
Useful resources

### Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

### How to use LaTex

Writing equations the easy way

### Study habits of A* students

Top tips from students who have already aced their exams