Question

MVT of f(x)=e^(-2x)

Answer 1

hey, how's it going?

Answer 2

I know the answer to this problem, but have gotten stuck when plugging in the values of a,b into the derivative

Answer 3

Good thank you

Answer 4

f'(x) = -2e^(-2x) Sorry Interval [0,3]
a @ 0 = 1
b @ 3 = e^-6

Answer 5

so what are you stuck on?

Answer 6

is this definitely the question as written, it doesn't look like the answer is going to be very "pretty"

Answer 7

f(x)=e^(-2x) Find all numbers that satisfy the conclusion of the Mean Value Theorem

Answer 8

on the closed interval [0,3]

Answer 9

ok so what are you stuck on

Answer 10

Getting the answer of -1/2ln[1/6(1-e^-6)]

Answer 11

do you know the formula of the mean value theorem? maybe you can tell me what part you're having trouble with

Answer 12

f'(c)=f(b)-f(a)/b-a or f(b)-f(a) = f'(c)(b-a)

Answer 13

do you want to tell me the steps you took and maybe i can see where you made a mistake?

Answer 14

I am not clear on how to incorporate the deriviative which is -2e^-2x using my a and b into this...

Answer 15

walking myself in circles

Answer 16

c is what you want to find

Answer 17

you have b and a and f(b) and f(a)

Answer 18

so f '(c) = -2e^(-2c) = you have the formula

Answer 19

the theorem means that there is an x-value c somewhere in the interval that makes the formula true

Answer 20

ok. so then would it e^(-6)-1=-2e^(-2c)(e^-6-1)

Answer 21

this being the average rate of change between these points, right

Answer 22

sorry last part (3-0)

Answer 23

looks right i think with your correction

Answer 24

Sometimes it helps to talk it out. Thanks a million!

Answer 25

did you end up getting the right answer?

Answer 26

Working through it now. YES!