Question

If f(x) is differentiable for the closed interval [-3, 2] such that f(-3) = 4 and f(2) = 4, then there exists a value c, -3 < c < 2 such that

Answer 1

http://mathworld.wolfram.com/RollesTheorem.html

Answer 2

can f be differentiable on the close interval?

Answer 3

closed*

Answer 4

can you show the work pls on how to do it?

Answer 5

what is your question by the way
to prove that c is in [-3,2] such that f is differentiable and f(-3)=f(2)

Answer 6

im not sure what they meant but the answer choices were
f(c) = 0


f '(c) = 0


f (c) = 5


f '(c) = 5

Answer 7

oh that's just easy
just read what rolle's theorem says
@ganeshie8 provided you with the theorem

Answer 8

you are just asked to complete what the theorem says
read it and see what you need to choose

Answer 9

ok give me a second

Answer 10

f '(c) = 0

Answer 11

I'm wondering if f can be differentiable at the end points of the interval
@ganeshie8 does that make sense?
may be right or left derivative exist

Answer 12

yes! that's what you need

Answer 13

Or would it be f(c)=0

Answer 14

well what did you read?

Answer 15

i read the link i understand now. may ii ask a few more questions

Answer 16

related to this question?

Answer 17

its another type i think

Answer 18

If f(x) = ι(x2 - 8)ι, how many numbers in the interval 0 ≤ x ≤ 2.5 satisfy the conclusion of the mean value theorem?


Three


Two


One


None

Answer 19

post in a different post
so others can help you

Answer 20

ok