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 c belongs to [a,b], then f(b)-__=________

Expert Answers
hala718 eNotes educator| Certified Educator

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

giorgiana1976 | Student

 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)

giorgiana1976 | Student

It is all you need, to fill in the blanks properly.

neela | Student

a) If f'(x) > 0, then in the interval {a,b} f(x) is increasing.

b) If f is a differentiable function in [a,b} and c belongs [a, b],

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