A Tibetan monk leaves the monastery at 7:00 am and takes his usual path to the top of the mountain, arriving at 7:00 pm. The following morning, he starts at 7:00 am at the top and takes another path back to the monastery, arriving at 7:00 pm. Show that there is some elevation that he reaches at the exact same time on both days. Hint: Let h1(t) be the monk’s elevation on the first day and h2(t) his elevation on the following day. Consider the function E(t) = h1(t) − h2(t).

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- anonymous

I don't have a clue what this question wants exactly

- dan815

okay

- dan815

interesting okay, so no matter the weird speed he takes the point is he finished both journies in 12 hours

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## More answers

- anonymous

Right lol

- dan815

we have to show there is always one point such that the elevation is the same at the same time

- dan815

ok hang on brb

- anonymous

Yeah np

- Astrophysics

IVT

- ganeshie8

Just show that E(0) and E(12) have opposite signs and use IVT

- anonymous

Intermediate Value theorem?

- Astrophysics

Yup

- anonymous

How do you know you have to use that tho?

- dan815

ok back

- dan815

now consider 2 functions h(t)

- ganeshie8

its bit hard to accept that there exists such a time where the elevations will be equal tho
also was wondering what if if the monk knows teleportation..

- dan815

|dw:1435215072294:dw|

- dan815

you see no matter what his function of height is over time

- dan815

there must be an intersection between h1(t) and h2(t)

- dan815

|dw:1435215133891:dw|

- ganeshie8

1 picture > 1000 words

- anonymous

Right...

- anonymous

LOL @ganeshie8

- dan815

|dw:1435215224870:dw|

- dan815

ya its hard to say in words lol but

- dan815

you can see, intuitively like no matter what function u can possibly think of, this intersection must exist somewhere

- dan815

and an intersection means the time and height was the same

- anonymous

Correct

- anonymous

And to prove that we gotta use the IVT?

- ganeshie8

yeah IVT is for mathematical proof
that picture is for convincing yourself why IVT works the way it does

- anonymous

E(t) has to change signs from + to - ?

- dan815

right, that would mean there is an intersection neat trick

- dan815

we know that h2(0) - h1(0) = Max height
and h2(12)-h1(12) = Negative of Max height

- anonymous

hmm... how do you know that again?

- dan815

that is what is given to us

- anonymous

Ohhh i just realized!! Sorry my bad! >.<

- dan815

we have 2 functions
h1(t) at t=0 , height is 0, t=12 hours height is max
h2(t) at t=0, height is max, t=12 hours height is 0

- anonymous

Mhmm I get it now

- ganeshie8

Another way to visulaize it is... assume that this monk knows magic and duplicated himself - one copy starts frm bottom and the other copy starts from top at the same time; since they both are walking towards each other on the same road, they will meet at some place for sure, no matter what their individual speeds are.

- dan815

haha i like that

- anonymous

Ahah right that makes sense lol xD nice visualization XD

- ganeshie8

ikr! everybody likes to duplicate themselves, especially before exams so that more work can be done in less time ;p

- ganeshie8

*likes the idea of

- Astrophysics

I think you may also need some help on knowing what exactly IVT is, so suppose f is continuous on [a.b] and let N be in (f(a),f(b)), where f(a) cannot = f(b). Then there exists a number c in (a,b), such that f(c) = N. Looks like bunch of mumbo jumbo so I'll draw a pic won't be as beautiful as dans drawing ;) |dw:1435215756830:dw| also if f(a) is negative and f(b) is positive (vice versa), then the equation f(x) = 0 has at least one root in (a,b). |dw:1435215895403:dw| hope that gives you an idea what is going on and you can relate this with your question now xD

- anonymous

Oh tell me about it!! Hahaha >.< I wish I had an extra week!! Lol might pull an all-nighter tonight :( which is the worst idea ever!!

- Astrophysics

Good problem though, not too difficult either just needs you to understand IVT really :P

- anonymous

That was a perfect explanation @Astrophysics!!! And beautiful drawings too ;P

- Astrophysics

I think what ganeshie said would work if the monk was an electron, and haha your welcome :)

- anonymous

- anonymous

Hahaha electrons dont duplicate... could be DNA though :P lol

- Astrophysics

True...but they can be in two places at once! See..at the quantum level nothing makes sense!

- anonymous

Hahaha thats a good point :DDD

- anonymous

Thanks again for all the help! :D

- Astrophysics

Np, have fun studying xD

- anonymous

Lol thanks... fun tho? XD

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