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Math Help - One Quick Mean Value Problem!!!

  1. #1
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    One Quick Mean Value Problem!!!

    1. Consider the function on the interval . Verify that this function satisfies the three hypotheses of Rolle's Theorem on the inverval.
    is ???? on ;
    is ???? on ;
    and ?????.
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  2. #2
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    Please someone help me?? or explain/ give hints!!!
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  3. #3
    MHF Contributor matheagle's Avatar
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    1 it is differentiable on the open interval

    2 it is continuous on the closed interval

    3 f(0)=f(4)=5

    SEE...
    http://en.wikipedia.org/wiki/Rolle's_theorem

    If a real-valued function ƒ is continuous on a closed interval [a,b], differentiable on the open interval (a, b),
    and ƒ(a) = ƒ(b), then there is some real number c in the open interval (a, b) such that f'(c)=0.

    So set 2x-4=0 and solve for x.
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  4. #4
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    Thanks matheagle.

    Quote Originally Posted by matheagle View Post
    1 it is differentiable on the open interval

    2 it is continuous on the closed interval

    3 f(0)=f(4)=5

    SEE...
    http://en.wikipedia.org/wiki/Rolle's_theorem

    If a real-valued function is continuous on a closed interval [a,b], differentiable on the open interval (a, b),
    and (a) = (b), then there is some real number c in the open interval (a, b) such that f'(c)=0.

    So set 2x-4=0 and solve for x.
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