Question

Determine whether the Mean Value Theorem can be applied to the function f(x) = lnx^2 on [1, sqr(e)]. If you can use the MVT, determine a value c that satisfies the theorem.

Answer 1

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Answer 2

f(x)=ln(x^2) or f(x)=(ln(x))^2

Answer 3

do you know what the mean value theorem is?

Answer 4

Do you know what criteria have to be satisfied to be able to apply the MVT?

Answer 5

f(x) = ln(x^2)
And yes, I understand the (f(b) - f(a))/ (b - a), but that's what I'm having trouble with... would it be (1/ (sqrt(e) - 1)? What do I do from there?

Answer 6

Before applying it, you need to see whether you can apply it. These need to be satisfied:
1. f is continuous on the closed interval [1, sqrt{e}]
2. f is differentiable on the open interval (1, sqrt{e})

Answer 7

Ohh. I got yes for both. Is this the correct way to approach the problem?
f'(x) = 2/x
2/x = 1/ (sqrt(e) - 1)
c = 2(sqrt(e) -1)

Answer 8

looks good

Answer 9

now is c in the interval given?

Answer 10

i believe so— it should be a positive number around 1.3 -sh

Answer 11

ok cool stuff