Does the Mean Value Theorem apply to
f(x)=(x+1)/x from [1,3]

Question

Does the Mean Value Theorem apply to 
f(x)=(x+1)/x    from [1,3]

precal · Answer

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amistre64 · Answer

is it continuous from 1 to 3?

precal · Answer

yes but continuity does not imply differentiablility

amistre64 · Answer

but it helps ....

precal · Answer

I know..

precal · Answer

I took the derivative and got  $$f \prime(x)=\frac{-1}{x^2}$$

dumbcow · Answer

nevermind

amistre64 · Answer

you have smooth curves, well behaved along intervals except for in that one spot ...

precal · Answer

I am looking for the c value that the Mean Value Thm guarantees

amistre64 · Answer

what your slope from 1 to 3?

precal · Answer

-1/3

amistre64 · Answer

the -x^(-2) Ds to get 2x^(-3)

amistre64 · Answer

when 2x^(-3) = -1/3 you got it

precal · Answer

I set that equal to the derivative to solve for x

amistre64 · Answer

when x^3 = 6 it looks like

amistre64 · Answer

-6 as the cace may be

amistre64 · Answer

is the cbrt (-6) in the interval?

precal · Answer

I got $$x=\sqrt{3}$$  for x.  Did I do something wrong?

amistre64 · Answer

i mighta did something wrong with these fat little fingers ...

dumbcow · Answer

i also get sqrt(3)  :)

amistre64 · Answer

your initial function is -x^(-2) right?

2x^(-3) is the derivative ... right?

amistre64 · Answer

i see what im doing, im confusing a few posts in this thing ...

amistre64 · Answer

ill go with sqrt(3) by default then :)

precal · Answer

ok thanks, I think I will stick with the math and forget the math movies.

amistre64 · Answer

everyone needs a hobby :)

precal · Answer

yes, I just don't have time to read anything other than math books.  Just not enough time.......