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 .
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?" 😁
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)
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) .
The theorem statement says N is a number between f(a) and f(b). In your example, -1 is not between sin(0) and sin(7pi/2), i.e., 0 and 1. Edit: I think you're mixing up what the theorem says. N being between f(a) and f(b) is in the antecedent, i.e., it's a precondition. *If* N is between f(a) and f(b), *then* there exists a c between a and b and so forth.
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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 .
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?" 😁
Finding your site helpful. I am encountering the IVT in calculus and prefer the way you demonstrate the theorem.
Great explanation! Thanks!
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)
This one is easy to understand you darn math sorcerer
IVT explanation I understood and could apply...great video!
Great to hear! I am glad this video helped someone!!
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) .
The theorem statement says N is a number between f(a) and f(b). In your example, -1 is not between sin(0) and sin(7pi/2), i.e., 0 and 1.
Edit: I think you're mixing up what the theorem says. N being between f(a) and f(b) is in the antecedent, i.e., it's a precondition. *If* N is between f(a) and f(b), *then* there exists a c between a and b and so forth.
What is the name of your pencil?
Ticonderoga
@@chrissmith9642 No, no. That's the name of the BRAND. The pencil's name is Joseph.
@@tungstendeliz4960 Smith. Joseph Smith
Hi! Isn't this the Bolzano Theorem?
Weird timing. I’m in a numerical analysis class and we just reviewed IVT yesterday for the bisection method 🤔
Genial explicación, entre el libro que estoy leyendo y esto, ya lo entendí. Estoy estudiando matemáticas para economía, también usamos algo! jaja.
it is obvious yet people don't remember it's application.
looks useless