Really a great thanks

  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. loll... how old are you kid?
     
  4. HallsofIvy

    HallsofIvy 40,673
    Staff Emeritus
    Science Advisor

    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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