How to determine if the derivative exist from the left and right of a absolute value

The video tutorial explores the concept of derivatives using the limit definition. It focuses on evaluating the derivative at x=1 by examining both left-hand and right-hand limits. The tutorial highlights the discontinuity in the denominator and demonstrates the calculation of derivatives from both sides. It concludes by explaining why the function is not differentiable at x=1 due to differing left and right-hand limits, emphasizing the importance of showing these limits rather than just identifying a corner in the graph.

How do the left-hand limit and right-hand limit differ at x = 1 for the function discussed?

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What steps would you take to show that the left and right-hand limits are not the same?

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