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April 19, 2015

Homework Help: Calculus (Continuity and Differentiability)

Posted by Mishaka on Saturday, November 12, 2011 at 3:43pm.

Okay. So I am given a graph of a derivative. From what I can gather, it looks like the function might be abs(x-2)-4. (I was not given an explicit function for g', just its graph.) The question then goes on to ask me:
Is it possible, impossible, or certain that the function g is continuous at x = 2? Explain.
Is it possible, impossible, or certain that the function g is differentiable at x = 2? Explain.
I am fairly sure that the answer to the second question is certain, since the graph of g' proves that at 2, the slope of the tangent line is -4. But, I am trying to figure out what kind of function would produce a corner in its derivative. Any help is appreciated!

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