# I got 3 questions!

1. Mar 11, 2007

### antibody

1. Suppose that f(a)=g(a) and the left-hand derivative of f at a equals the right-hand derivative of g at a. Define h(x)=f(x) for x<=a, and h(x)=g(x) for x>=a. Prove that h is differentiable at a.

2. Let 0<B<1. Prove that if f satisfies /f(x)/ >= /x/^B and f(0)=0, then f is not differentiable at 0.

the sign / / is absolute value.

3. Let f(x)=x^n for x>=0 and let f(x)=0 for x<=0. Prove that f^(n-1)exists and find a formula for it, but that f^(n) (0) does not exist.

Can someone help me out with these problems? thx a lot!!!

2. Mar 11, 2007

### cristo

Staff Emeritus
You need to show some work on homework questions before we can help you.

3. Mar 11, 2007

### Tom Mattson

Staff Emeritus
Yep. That, and homework goes in the Homework Help section, not the Math section.

So, antibody, let's see whatcha got so far.

4. Mar 11, 2007

### antibody

for the second one , i know how to prove the converse, like let B>1, if f satisfies /f(x)/ <=/x/^B, prove that f is differentiable at 0,

this one will be easier, first let x=0 then f(0)=0, and i know to prove some fn is differentiable at some point x, it means to prove lim(h->0) f(x+h)-f(x) /h = some number( here is 0 since the prob has given)

i guess i can do the same thing to the second one, but i m not sure how to write a religious proof.

5. Mar 11, 2007

### antibody

and same thing happens to quesntion no.3 .......

if the question gives me some precise function, i probably can solve it,
but this one i am still working on it, my idea is
x^n when x>=0
f(x)=
0 when x<=0

so the f ' (x) = n x^(n-1) when x>0 and f ' (x)=0 when x<0 then use the left and right limit to see if f ' (x) exists when x=0. Right?

and again..i am not very familiar with this kind of proof right now,, since we just spent a week on this topic, and i am not sure when we need to use delta-epsilon proof on the question...