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IVT/MVT (Calculus) watch

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    I dont understand IVT at all, does anyone understand any of these?Attachment 726858
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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 f is continuous on some interval I, like I=[a,b], then f must take on every single value between f(a) and 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.
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    I can do exercise 1 now, but still dont understand the rest
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    (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
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    (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 c?
 
 
 

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