Name: Intermediate value theorem | Existence theorems | AP Calculus AB | Khan Academy
Uploaded: 2022-07-05T14:15:06.000Z
Duration: 8 min 5 s
Description: Thousands of YouTube videos with English-Chinese subtitles! Now you can learn to understand native speakers, expand your vocabulary, and improve your pronunciation...

Future simple

- [Voiceover] What we're gonna cover in this video

Which, despite some of this mathy language you'll see

possibly the most intuitive theorem you will

we'll all appreciate that it's pretty obvious.

But, I think the conceptual underpinning here is

So the theorem tells us that suppose F is a function

continuous at every point of the interval

the closed interval, so we're including A and B.

So it's continuous at every point of the interval A, B.

Suppose F is a function continuous at every point

F is continuous at every point of the interval

So that means it's got to be for sure defined

And the limit of the function that is recorded at that point

should be equal to the value of the function of that point.

And so the function is definitely going to be defined

So it's definitely going to have an F of A

And they tell us it is a continuous function.

So if you're trying to imagine continuous functions

And, if it's continuous we need to be able to

get to the other, the value of the function

oops, I got to pick up my pencil do something like that,

Whoa, okay, pick up my pencil, go down here,

over the closed interval A, B looks like.

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Intermediate value theorem | Existence theorems | AP Calculus AB | Khan Academy

essentially

potential

assume

obvious