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Math Help - continuous functions and differentiability

  1. #1
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    continuous functions and differentiability

    g(x)=

    x+b, x<0
    cosx, x greater than or equal to 0

    Is there a value for b that will make g(x) continuous at x=0? Is there a value that will make g(x) differentiable at zero? If there is, what is it? If not, why not? Give reasons for your answeres.

    Thanks
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    Forum Admin topsquark's Avatar
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    Quote Originally Posted by Mr_Green View Post
    g(x)=

    x+b, x<0
    cosx, x greater than or equal to 0

    Is there a value for b that will make g(x) continuous at x=0? Is there a value that will make g(x) differentiable at zero? If there is, what is it? If not, why not? Give reasons for your answeres.

    Thanks
    You need to find a value for b. What is the definition of continuous? What has to happen at x = 0?

    For the second part, take the derivative of your function. In order for the derivative to exist at x = 0 the derivative of g(x) must be continuous at x = 0. Is it?

    -Dan
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  3. #3
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    Here is the graph of one such function. It should answer both questions.
    Attached Thumbnails Attached Thumbnails continuous functions and differentiability-contp.gif  
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