Today I am asked to convince you the intermediate value theorem, and I’d like to use some simple example in our daily life to make it.I believe the running in a filed can make sense.
Mike is a runner who always run after class. He always run 200m in 5min every day.Let the 200m track is straight or curl whatever.But if Mike need to reach the end of the track, he must go through the each point of the track in some time during the 5min, even though the track is longer than 200m and you surpass the end of the track and go back at last .Coz the Mike cannot fly or something like take a cab to prevent you from going through the any point of 200m to reach the end.
As the intermediate value theorem
—–{if a continuous function f with an interval [a, b] as its domain takes values f(a) and f(b) at each end of the interval, then it also takes any value between f(a) and f(b) at some point within the interval.}
Each point is the f(x) in the theorem and the time is the x in it.The the f(x) must go through all the value before he get the f(b).So the theorem hold water.