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Thread: question about Mean Value Theorem

  1. #1
    Senior Member Vinod's Avatar
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    question about Mean Value Theorem

    Hello Forumites,
    I want to show that f(x)= $cos^2(x)+cos^2(π/3+x)-cos(x)*cos(π/3+x)$ is a constant function. What is it's value?
    Solution

    Now,to prove f(x) is a constant function,f'(x)=0 but f'(x)=-sin(2x)-sin(2*(3x+π)/3)+sin((6x+π)/3).Now what would be a interval I in which f(b)= f(a)?
    Last edited by Vinod; Sep 14th 2018 at 09:54 PM.
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  2. #2
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    Re: question about Mean Value Theorem

    Quote Originally Posted by Vinod View Post
    Hello Forumites,
    I want to show that f(x)= $cos^2(x)+cos^2(π/3+x)-cos(x)*cos(π/3+x)$ is a constant function. What is it's value?
    Solution

    Now,to prove f(x) is a constant function,f'(x)=0 but f'(x)=-sin(2x)-sin(2*(3x+π)/3)+sin((6x+π)/3).Now what would be a interval I in which f(b)= f(a)?
    If you just work with f(x) and make use of the expansion of cos(a+b) = cos(a) cos(b)-sin(a) sin(b) and the Pythagorean identity, you'll find that f(x) = 3/4 which is constant.
    I can't see any need to find f'(x).
    Thanks from topsquark and Vinod
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  3. #3
    MHF Contributor

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    Re: question about Mean Value Theorem

    What, exactly, are you trying to prove? If f(x) is constant, it has the same value everywhere and its derivative is 0 everywhere. There is NO particular interval to work with nor is the "mean value theorem" particularly relevant here.
    Thanks from topsquark
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