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Inequality with mvt

  1. Dec 5, 2008 #1
    1. The problem statement, all variables and given/known data

    -x<sin(x)<x

    2. Relevant equations

    show the inequality using the mean value theorem.

    3. The attempt at a solution
    i try to find c but i keep getting tan(x) as the solution.
     
  2. jcsd
  3. Dec 5, 2008 #2

    gabbagabbahey

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    If you show me what you've tried, I can help you better.
     
  4. Dec 5, 2008 #3
    i had:

    f(x)=sin(x) a=-x b=x

    f(x)-f(-x)= f'(c) (x+x)
    sin(x) = sin(x)=cos(c) (2x)
    2sin(x)=2cos(xc)
    tan(x)=c

    i don't know if that's right, but i don't get the result.

    i would appreciate your help.
     
  5. Dec 5, 2008 #4

    gabbagabbahey

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    First, [itex]2x \cos (c) \neq 2 \cos(cx)[/itex] and second [tex]\frac{\cos(cx)}{\cos (x)}\neq c[/tex]!

    Try again, but this time use a=0 and b=x.

    What do you know about the maximum and minimum values of cosine of any number?
     
  6. Dec 6, 2008 #5
    ok, now i got:

    f(x)=sin(x) a=0 b=x

    f(x)-f(0)= f'(c) (x-0)
    sin(x) =cos(c) (x)
    sin(x)/x=cos(c)

    im stucked there...
    i don't know what you mean with the the maximum and minimum values of cosine of any number.
     
  7. Dec 6, 2008 #6

    gabbagabbahey

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    Well, cosine is a periodic function that is never greater than 1 or less than negative 1....ring a bell?

    That means that [itex]-1\leq \cos (c) \leq 1[/itex] and so....
     
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