Question

What are the 3 requirements a function must meet in order to be able to use Rolle's Theorem? I know the first 2 are "Is the function continuous?" and "Is the function differentiable?", what's the 3rd requirement?

Answer 1

look like the if part of rolle's theorem
that which is in the if part must be the part in which the function meets as a requirement to apply rolle's theorem

Answer 2

If I is continuous on a closed interval [a,b]
and
differentiable on the open interval (a,b)
and
if f(a)=f(b),
then there is at least one point c in (a,b) such that f'(c)=0.

Answer 3

Do you see 3 requirements?

Answer 4

And remember you only care about satisfying the if part
to see Rolle's theorem applies.

Answer 5

that first line "If f" <-- not "If I"

Answer 6

So f(c) must equal 0 at some point on the function?

Answer 7

Only look at the if part to see what is required to apply the theorem

Answer 8

requirement number 1) f is continuous on [a,b]

Answer 9

requirement number 2) is?

Answer 10

Differentiable on open interval.

Answer 11

And so the 3rd requirement is the function must = 0 at some point? Correct me if I'm wrong...

Answer 12

f(a)=f(b)

Answer 13

f(a)=f(b) is all in the if part

Answer 14

also not all

Answer 15

For example say we have f(x)=x^2.
f is continuous on [-3,3]
f is differntiable on (-3,3)
f(3)=f(-3)
So we can apply rolle's theorem
That is there is at least one value c in the interval (-3,-3) such that f'(c)=0
Well f'(x)=2x
So 2x=0 when x=0
0 is indeed in between -3 and 3

Answer 16

oh okay... :) Thanks!

Answer 17

do you need help with anything?

Answer 18

Nah I'm cool. Thanks for asking though :)