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Thread: question about differential and discontinuity

  1. #1 question about differential and discontinuity 
    Forum Bachelors Degree
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    Hello! I got something that do not understand
    Here is a picture:


    Why this function is not differentiable in x=0 ?

    It can be seen that the slopes of both sides of the function are same? Why it is not differentiable at x=0?

    Thanks in advance.


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  3. #2 Re: question about differential and discontinuity 
    Forum Professor wallaby's Avatar
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    Quote Originally Posted by scientist91
    It can be seen that the slopes of both sides of the function are same? Why it is not differentiable at x=0?
    Not quite the same. The slope of the graph for all values of x > 0 is positive, while the slope of the graph for all values of x < 0 is negative. So the limit, of the derivative, approaches different values from each direction. As far as i know this is why the derivative does not exist at x = 0.


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  4. #3 Re: question about differential and discontinuity 
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    Quote Originally Posted by wallaby
    Quote Originally Posted by scientist91
    It can be seen that the slopes of both sides of the function are same? Why it is not differentiable at x=0?
    Not quite the same. The slope of the graph for all values of x > 0 is positive, while the slope of the graph for all values of x < 0 is negative. So the limit, of the derivative, approaches different values from each direction. As far as i know this is why the derivative does not exist at x = 0.
    Thank you for the post and sorry I post wrong diagram. Here is the correct one:



    The blue dot is "hole" in the graphic of the function.

    The slopes are same. Why the it is not differentiable at x=0 ?
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  5. #4 Re: question about differential and discontinuity 
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    Quote Originally Posted by scientist91
    Quote Originally Posted by wallaby
    Quote Originally Posted by scientist91
    It can be seen that the slopes of both sides of the function are same? Why it is not differentiable at x=0?
    Not quite the same. The slope of the graph for all values of x > 0 is positive, while the slope of the graph for all values of x < 0 is negative. So the limit, of the derivative, approaches different values from each direction. As far as i know this is why the derivative does not exist at x = 0.
    Thank you for the post and sorry I post wrong diagram. Here is the correct one:



    The blue dot is "hole" in the graphic of the function.

    The slopes are same. Why the it is not differentiable at x=0 ?
    It is differentiable at x=0 unless it is (freakishly) defined to be discontinuous at that point. I suppose that's the point of the blue dot.
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