Fill in the blanks 1) If f'(x)>0 on the interval [a,b], then f is______________ 2) If f is a differentiable function on the interval [a,b] and...

 1) If f'(x)>0 on the interval [a,b], then f is increasing on that interval [a,b].

2) If f is a differentiable function on the interval [a,b] and c belongs to [a,b], then

f(b)-f(a)=f'(c)(b-a)

We've used the Mean Value Theorem and you could also write:

f'(c)=[f(b)-f(a)]/(b-a)