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Thread: Mean Value Theorem

  1. #1
    Mar 2006

    Mean Value Theorem

    I am having a problem with coming out with the right answer for the following problems, please help.

    Using the Mean Value Theorem. If f(x)=sin(x) on the interval [1, 1.15] what is c.
    okay the Mean Value Thoerem is f'(c) = f(b)-f(a)/b-a
    so I have 1.15-1/.15, so tell me if I'm on the right track,if not please help.

    Next problem
    Sin(x)+ln y and 0<x<pi/2, using implicit differntiation, what is dy/dx.
    Where do I start?

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  2. #2
    MHF Contributor
    Oct 2005
    On the first one, you are on the right track, but one thing. You found the y-coordinate of c, which is f(c). They want to know the x-coordinate, c. So, set sin(x)=f(c) (the value you got) and solve for c.

    $\displaystyle sin(c)=\frac{sin(1.15)-sin(1)}{1.15-1}$

    On the second one, you know that sin(x)+ln(y) must equal some constant correct? So set it up like this.

    $\displaystyle sin(x)+ln(y)=c$
    $\displaystyle cos(x)+\frac{1}{y}*\frac{dy}{dx}=0$

    See how that works? I'm sure you can finish it from there.
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