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The position function for the trip up is .
The time taken for run up the mountain is minutes.
The position function of trip up at the foot of the mountain is .
The position function of trip up at the top of the mountain is .
The position function for the trip down is .
The time taken for run down the mountain is minutes.
The position function of trip down at the top of the mountain is .
The position function of trip down at the foot of the mountain is .
The function is .
Find .
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The elevation at the foot of the mountain is lower than at the top of mountain.
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Find .
The elevation at the half way point up of the mountain is higher than the foot of mountain.
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The position functions and are continuous functions.
If two functions and are continuous, then also continuous.
Intermediate value theorem:
If is continuous on the closed interval , , and is any number between and , then there is at least one number in such that .
and .
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By intermediate value theorem,there must be some in ,such that ..
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is the time between and .
At time he passed the same place at same time on Saturday.
At time he passed the same place at same time on Saturday.
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