Question

could someone explain Rolle theorem?

Answer 1

yes....

Answer 2

it is the mean theorum but for a flat line.... really.....

Answer 3

the mean theorum states that any slope between two points can be moved to a spot on the curve where it only touches at one point right?

Answer 4

the Rolle theorum states that if the slope between two poits is a flat horizontal line, then there is a point on the curve that the flat line will only touch in one spot......

Answer 5

ok thanks, how is it represented mathematically?

Answer 6

...that I dont know ;)

Answer 7

if an interval I exists and is continuous between it end points and the interval I [a,b] has a slope of zero between f(a) and f(b) then there exists a point in the interval [a,b] called "c" such that the f'(c) = 0....matbe like that :)

Answer 8

oh so in essence it's similiar to the mean value theorem?

Answer 9

in essense...it IS the mean value theorum ;) only with a flat line. Why we need it to have its own name is a mystery to me....

Answer 10

yeah I wonder also I am gonna send you a question and u solve it n show me the steps

Answer 11

if I got the time, I gotta get to class in 30 minutes :)

Answer 12

ok u gonna be back anytime soon?

Answer 13

3 hours..if anything. post it up on the main side over there and see if anyone bites.

Answer 14

or let me see it and ill let you know if I got the time :)

Answer 15

ok

Answer 16

\[let f:[-1,1]rightarrowR be such that\]

Answer 17

let f:[−1,1]rightarrow R be such that

Answer 18

let f(-1) to f(1) be.....

Answer 19

\[f(x)= x^2 - 1/(1+x^2)\]

Answer 20

plug in -1 and solve: f(-1) = 0

plug in 1 and solve: f(1) = 0

Answer 21

yes and show that f satisfies all the conditions for the application of Rolle's theorem

Answer 22

since the bottom of the function is never 0, we have no restrictions there and the function is continuous thruout the interval...

Answer 23

if we can find the x = c such that f'(c) = 0 ..... then that shuold solve it.

Answer 24

Rolles theorum doesnt tell you HOW to find "c", just that itlll exist :)

Answer 25

are there any values of x in the interval [-1,1] that we should avoid using? I dont see any, so it is continuous right?

Answer 26

yea it's continous

Answer 27

what value of x will make the denominator go to zero?

1+x^2 = 0 .....none, nade, zip, ziltch.... its consinuous :) so there must be a c value in the interval [-1,1] that satisfies Rolles theorum

Answer 28

so it's saying find all c which satisfy the conclusion of Rolle's them

Answer 29

if you want to find it, yo could look for the hgihest or lowest value of f(x) and that would be it; or take the derivative and make it equal to 0 right?

Answer 30

oh, so take the defferential of f(x) and equate it to zero

Answer 31

n solve for x?

Answer 32

yep, at f'(x) = 0 we have what they call "critical points" is is when the slope of the curve becomes "0"...a horizontal line

Answer 33

yes..

(1+x^2)(2x) - (x^2 -1)(2x) = 0

Answer 34

4x = 0....when x = 0

Answer 35

f(0) = -1 :)

Answer 36

ok thanx, have a productive class

Answer 37

Ciao:)

Answer 38

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