Thread: Using IVT (Int Value Therom) on a Hill

(Click the picture to see the problem and what I have done so far)

Originally Posted by Chaim

(Click the picture to see the problem and what I have done so far)

So you have defined two different functions. You have



and



For these functions to be compatable they must agree on where you define the top and the bottom.

If you defince the top to 1 and the bottom to be 0 then you must have these values



and



So you get the two functions



Now if you define their difference it will only exist on the intersection of their domains!



But notice that



Since f is continous the intermediate value theorem says there exists a such that

So we get that



So the hiker was at the same place at the same time.

Note: Since the function is linear would could solve for the value of t explicitly, but the power of the IVT is we don't have to be able to find it.