The Intermediate Value Theorem

This is a full introduction to the Intermediate Value Theorem.

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[Strikerfm]

I hope you read this: I purchased your Udemy college algebra course and Trig course. I passed college algebra with a A.(after previously failing the class). Your trig course helped me blow through my Trig class. I am currently studying pre cal and we are learning about this theorem right now. you took me from remedial math courses to acing college level classes . Thank you .

[MrJegerjeg]

That reminds me of a conversation I had with a friend a couple of days ago. She is on a diet, and she is happy that she went down to 65 Kg. Me as a tall man I am in the range of 90 Kg. So I said, "I can't remember the last time I was 65 Kg". She was confused and I added "Do you think I was more than 65 Kg when I was born?" 😁

[davidnelson]

Finding your site helpful. I am encountering the IVT in calculus and prefer the way you demonstrate the theorem.

[wqltr]

This theorem has nice visual intuition too.
If you imagine the lines x = a and x = b, starting at (a, f(a)) and going to (b, f(b)), without letting go of your pencil try to avoid intersecting the line y = N s.t. f(a)<N<f(b). By I.V.T. it should'nt be possible.

[antonbashkin]

This one is easy to understand you darn math sorcerer

[tomsdailystudy]

IVT explanation I understood and could apply...great video!

[gaMesMarcoGloazzo]

Hi! Isn't this the Bolzano Theorem?

[rounakdas]

If I choose f = sinx in [0, 7π/2] then there exists some pt on this interval where the function value does not belong to (f(0), f(7π/2)) in this interval which contradict the theorem statement, just for example at x = 3π/2 f has value -1 . Which does not in (0, 1) .

[dAntony]

Weird timing. I’m in a numerical analysis class and we just reviewed IVT yesterday for the bisection method 🤔

[ujwalsmanhas]

it is obvious yet people don't remember it's application.

[OscarHernandez-ulgo]

Genial explicación, entre el libro que estoy leyendo y esto, ya lo entendí. Estoy estudiando matemáticas para economía, también usamos algo! jaja.