Question

does this function satisfies rolle's theorem ?

Answer 1

no

Answer 2

why not?

Answer 3

@gupta101 ?

Answer 4

yeah it seems is not diffentiiable on x = 2 but how do explain that

Answer 5

First define what Rolle's theorem is.

Answer 6

hmm im beign asked on 0,4 interval

Answer 7

well a function must be differentiable and continuos on the interval

Answer 8

and f(a) = f(b)

Answer 9

its easier to google what it is, its basically a special case for the mean values theorem

Answer 10

does f(1) = f(3)?
is it cont/dif on (1,3)?

Answer 11

hmm nope the interval is [0,4]

Answer 12

on [0,4] it satisfies f(a) = f(b)

Answer 13

1. continuous on [a,b]
2. differentiable on (a,b)
3. f(a) = f(b)
4. number c in (a,b) where f'(c) = 0

niot that hard to define

Answer 14

that's not the definition

Answer 15

1,2,3 imply 4

Answer 16

That is rolle's theorem.

Answer 17

its not...reread it

Answer 18

if 1 and 2 and 3 then 4

Answer 19

ok so 2 is a problem, @Bryan11

Answer 20

So you want to prove its not continuous there?

Answer 21

what def of continuity do you use, sequential or \(\delta -\epsilon\)

Answer 22

Oh, i wrote 4 as part of it, whoops. 1,2,3 \(\therefore\) 4

Answer 23

;)

Answer 24

@Bryan11 what is your def of continuity?

Answer 25

hmmm when the function has no holes, or jumps

Answer 26

what about |x| is it continuous?

Answer 27

nope

Answer 28

i mean yes abs(x) is continuous but not diffrentiable at x=0