# Question about fundamental thm calc part 1

1. Dec 3, 2011

### Miike012

If f is continuous on [a,b] then the fucntion g defined by
g(x) = ∫f(t)dt a <= x <= b is continuous on [a,b] and differentiable on (a,b) and g' = f

Question....

If f is continuous on [a,b], then why is g only differentiable on (a,b)?
This does not make sence... if g' = f g should be diff on [a,b] after making the first statement "f is continuous on [a,b]"

2. Dec 3, 2011

### micromass

The thing is that differentiability is often only defined on open intervals. This is likely what your text has done.

If you want g to be differentiable on [a,b], then you need to have a definition for differentiability on closed intervals.

Mod note: as this is not a homework problem, I mover it to the math forums.