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Really a great thanks

  1. Jan 8, 2004 #1
    again, i've another question i wish it is the last.
    it is about "Mean Value Theorem",

    * if u and v are any real numbers, then, prove that:
    |sin(u)-sin(v)|<=|u-v|

    * Prove that [(1+h)^(1/2)] < [1+(h/2)], for h>0

    * Suppose that f'(x)=g'(x)+x for every (x) in some interval (I), how different can the function (f) and (g) be

    I don't know from where to start and i would like you to know that i'm in exams' days, and that's not assignment

    thank you alot for your efforts
     
  2. jcsd
  3. Jan 8, 2004 #2

    loll... how old are you kid?
     
  4. Jan 9, 2004 #3

    HallsofIvy

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    Staff Emeritus
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    Prudens Optimus, why "lol"? These seem like reasonable questions to me.

    moham_87, since you say that these are about the "mean value theorem", how about using that?

    Mean Value Theorem: "If f is continuous on [a,b] and differentiable on (a,b) then there exist c in [a,b] such that
    f'(c)= (f(b)- f(a))/(b-a)."

    In the first problem, f(x)= sin(x). What is f'(x)? What is the largest possible value of f'(x)?

    In the second problem, f(x)= (1+h2)1/2. What is f'(x)? What is the largest possible value of f'(x)?

    In the third problem, if f'(x)=g'(x)+x , what is f(x)?
     
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