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# IVT/MVT (Calculus) watch

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1. I dont understand IVT at all, does anyone understand any of these?Attachment 726858
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2. (Original post by Amyherdman)
I dont understand IVT at all, does anyone understand any of these?
All IVT says is that if your function is continuous on some interval , like , then must take on every single value between and .

So begin with Q1. The polynomial is obviously continuous on any interval, so that includes [1,4], hence you can use IVT to prove that there is a root in this range. Use the hint further to show that this is the only root.
3. I can do exercise 1 now, but still dont understand the rest
4. (Original post by Amyherdman)
I can do exercise 1 now, but still dont understand the rest
OK, exercise 2 requires you to apply the min-max theorem as said. What does the theorem say?
5. (Original post by RDKGames)
OK, exercise 2 requires you to apply the min-max theorem as said. What does the theorem say?
If its continuous between [a,b]. Then there exists m,M belonging to R, and x1, x2 belonging to [a,b] such that f(c) = 0

m = f(x1) ≥ f(x) ≥ f(x2) = M
6. (Original post by Amyherdman)
If its continuous between [a,b]. Then there exists m,M belonging to R, and x1, x2 belonging to [a,b] such that f(c) = 0

m = f(x1) ≥ f(x) ≥ f(x2) = M
This doesn't make much sense. What's ?

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