# Differentiability on a closed interval

1. Jan 17, 2010

### Niles

1. The problem statement, all variables and given/known data
Hi all

I wish to show differentiability of g(x)=x on the interval [-pi, pi]. This is what I have done:

$$g'(a) = \mathop {\lim }\limits_{h \to 0} \frac{{g\left( {a + h} \right) - g\left( {a} \right)}}{h} \\ = \mathop {\lim }\limits_{h \to 0} \frac{h}{h} \\ = 1,$$

for a in the interval [-pi,pi]. Hence we see that the derivative is 1 on this interval.

Am I correct?

Best,
Niles.

2. Jan 17, 2010

### Dick

Sure, that's great.