Suppose a mountain climber ascends a mountain path, starting at 7 am and arrivin

ID: 2835622 • Letter: S

Question

Suppose a mountain climber ascends a mountain path,

starting at 7 am and arriving at the first way station at 4 pm, where he stays

the night. In the morning he realizes the battery of his digital is drained and,

more importantly, that he forgot the spare batteries at the base camp. So

he leaves the way station at 7 am and hikes back to the base camp, arriving

at 4 pm. Use the Intermediate Value Theorem to argue that there is some

point along the path that he crossed at the same time on each day.

Hint: Consider the function (a1(t) - a2(t)) where a1(t) and a2(t) tell us the climber's

altitude after (t) hours of hiking on the first and second day, respectively.

Full work please, clear writing to read.

let a1(t), a2(t) is altitude of the climber after t hours on first and second day respectively.

let a(t) = a1(t)-a2(t)=>

a1(0) =0, a1(9) = h,

a2(0) = h, a2(9) = 0,

a(0)=-h, a(9) = h

=> by IMV theorem, there exists a t in[0,9] such that a(t) =0

thus proved

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