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IVT/MVT (Calculus)

I dont understand IVT at all, does anyone understand any of these?
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Original post by Amyherdman
I dont understand IVT at all, does anyone understand any of these?


All IVT says is that if your function ff is continuous on some interval II, like I=[a,b]I=[a,b], then ff must take on every single value between f(a)f(a) and f(b)f(b).

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.
(edited 6 years ago)
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Amyherdman
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I can do exercise 1 now, but still dont understand the rest
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?
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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
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 cc?

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