Going Crazy over this Mean Value Theorem Question!!!  TOPIC_SOLVED

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Going Crazy over this Mean Value Theorem Question!!!

Postby kittie21 on Fri Jan 28, 2011 10:25 pm

Okay so the question is asking to show that for 0<x<y, sqrty - sqrtx < (y - x)/(2 sqrt x) (using the mean value theorem)

I think I have some valuable information pertaining to the question...but I am so confused about how to solve it I could just be pulling numbers out of nowhere in a desperate attempt to feel smart!

I have the slope of the tangent for sqrty - sqrt x = -sqrt y / y and the slope of the tangent for (y - x)/(2 sqrt x) = -(1/2y)/ y But not sure what I do with this information! any help would be amazingly appreciated!
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Re: Going Crazy over this Mean Value Theorem Question!!!

Postby Martingale on Fri Jan 28, 2011 10:41 pm

kittie21 wrote:Okay so the question is asking to show that for 0<x<y, sqrty - sqrtx < (y - x)/(2 sqrt x) (using the mean value theorem)

I think I have some valuable information pertaining to the question...but I am so confused about how to solve it I could just be pulling numbers out of nowhere in a desperate attempt to feel smart!

I have the slope of the tangent for sqrty - sqrt x = -sqrt y / y and the slope of the tangent for (y - x)/(2 sqrt x) = -(1/2y)/ y But not sure what I do with this information! any help would be amazingly appreciated!




between and

let

...
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Re: Going Crazy over this Mean Value Theorem Question!!!

Postby kittie21 on Fri Jan 28, 2011 10:45 pm

Thanks for the response! But I am not sure what I am supposed to do with this f(t) = sqrt t ... how does that fit in with the question? Am I using substitution with the t?
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Re: Going Crazy over this Mean Value Theorem Question!!!

Postby Martingale on Fri Jan 28, 2011 10:53 pm

kittie21 wrote:Thanks for the response! But I am not sure what I am supposed to do with this f(t) = sqrt t ... how does that fit in with the question? Am I using substitution with the t?

Martingale wrote:


between and

let

...







...
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Re: Going Crazy over this Mean Value Theorem Question!!!

Postby kittie21 on Sat Jan 29, 2011 1:44 am

...so.. the derivative of c, which is 1/2sqrt c should equal the slope of the tangent, sqrt y/ y. It makes sense in theory, but how do I make them equal eachother? Am I now supposed to solve for one of the variables? But there is two of them. I do not understand the next step. Thanks for your help so far though!
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Re: Going Crazy over this Mean Value Theorem Question!!!

Postby Martingale on Sat Jan 29, 2011 2:05 am

kittie21 wrote:...so.. the derivative of c, which is 1/2sqrt c should equal the slope of the tangent, sqrt y/ y. It makes sense in theory, but how do I make them equal eachother? Am I now supposed to solve for one of the variables? But there is two of them. I do not understand the next step. Thanks for your help so far though!


Martingale wrote:





...




you want to show that

To get the above you need to answer for what value of is as large as possible...or
for what value of is as small as possible.

remember...
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Re: Going Crazy over this Mean Value Theorem Question!!!

Postby kittie21 on Sat Jan 29, 2011 4:47 pm

Soo... can I designate numbers to the value of x and y as long as they fit in with 0<x<y? How do I know which numbers to use to do that?
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Re: Going Crazy over this Mean Value Theorem Question!!!

Postby kittie21 on Sat Jan 29, 2011 4:52 pm

okay so, the f(y)-f(x)/y-x has to be greater than 0, which means that b-a > 0 which means that the divisor must be positive so that the answer stays above zero, so b>a! I don't need to find an exact answer, do I?!
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Re: Going Crazy over this Mean Value Theorem Question!!!

Postby kittie21 on Sat Jan 29, 2011 4:59 pm

I mean , so y>x...but i just realized that that is what the 0<x<y was saying anyways. nevermind. I am still confused!
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Re: Going Crazy over this Mean Value Theorem Question!!!

Postby Martingale on Sat Jan 29, 2011 5:02 pm

kittie21 wrote:okay so, the f(y)-f(x)/y-x has to be greater than 0, which means that b-a > 0 which means that the divisor must be positive so that the answer stays above zero, so b>a! I don't need to find an exact answer, do I?!


I'm not sure what you are trying to accomplish with the above post.


I think at this point, if you don't see how to finish, you should look in your book to see examples of how the Mean Value theorem can be used. If I give one more hint I'll be doing the entire problem. (which doesn't really help you)
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