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    Calculus Help

    I'm asked to list the conditions where a function would not be differentiable, graph them and also explain why they are not differentiable. Can anyone point me in the righth direction.





    n/m found the answer

    Corner, discontinuity, and vertical tangent

    n/m again now i'm having trouble finding the reason why they cannot be differentiable. Any help is appreciated
    Last edited by JonathanEyoon; January 29th 2008 at 11:34 AM.
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    Quote Originally Posted by JonathanEyoon View Post
    Corner, vertical tangent
    Limits don't exist?
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    Quote Originally Posted by JonathanEyoon View Post
    I'm asked to list the conditions where a function would not be differentiable, graph them and also explain why they are not differentiable. Can anyone point me in the righth direction.

    n/m found the answer

    Corner, discontinuity, and vertical tangent

    n/m again now i'm having trouble finding the reason why they cannot be differentiable. Any help is appreciated
    Good question: There are many ways to think about this. Think about this way... the derivative measures the rate of change. If there is a point of discontinuity, then there is lack of connection between one point and the next. This removes the possibility of having any change at all.

    A point is continuous if you can find the limiting value of the function as x approaches that point. In the situation of a cusp, it is continuous, but the definition of the derivative does not hold. The following example shows the absence of a derivative for f(x)=|x| at x=0

    lim_{h \rightarrow 0} \frac{f(x+h) - f(x)}{h} = \frac{|h|}{h} \Rightarrow \frac{0}{0} ~ DNE
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