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

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

Mathematics
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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hey, how's it going?
I know the answer to this problem, but have gotten stuck when plugging in the values of a,b into the derivative
Good thank you

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Other answers:

f'(x) = -2e^(-2x) Sorry Interval [0,3] a @ 0 = 1 b @ 3 = e^-6
so what are you stuck on?
is this definitely the question as written, it doesn't look like the answer is going to be very "pretty"
f(x)=e^(-2x) Find all numbers that satisfy the conclusion of the Mean Value Theorem
on the closed interval [0,3]
ok so what are you stuck on
Getting the answer of -1/2ln[1/6(1-e^-6)]
do you know the formula of the mean value theorem? maybe you can tell me what part you're having trouble with
f'(c)=f(b)-f(a)/b-a or f(b)-f(a) = f'(c)(b-a)
do you want to tell me the steps you took and maybe i can see where you made a mistake?
I am not clear on how to incorporate the deriviative which is -2e^-2x using my a and b into this...
walking myself in circles
c is what you want to find
you have b and a and f(b) and f(a)
so f '(c) = -2e^(-2c) = you have the formula
the theorem means that there is an x-value c somewhere in the interval that makes the formula true
ok. so then would it e^(-6)-1=-2e^(-2c)(e^-6-1)
this being the average rate of change between these points, right
sorry last part (3-0)
looks right i think with your correction
Sometimes it helps to talk it out. Thanks a million!
did you end up getting the right answer?
Working through it now. YES!

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