1. ## Mean Value Theorem

is this statement true?
If f'(x)=0 for all $x$ in an interval (a, b), then f(x)=0 for all x in the interval (a, b).

2. Originally Posted by Baatata
is this statement true?
If f'(x)=0 for all $x$ in an interval (a, b), then f(x)=0 for all x in the interval (a, b).
what would be the value of f'(x) in (a,b) if f(x) = 1 ?

3. Originally Posted by Baatata
is this statement true?
If f'(x)=0 for all $x$ in an interval (a, b), then f(x)=0 for all x in the interval (a, b).
No, f could be another constant.

4. If f(x)=0 implies that f'(x)=0 .
However, the same can be said for any constant c.
Thus, f(x) = c implies that f'(x)=0.