Ah, see here—the graph of |x| makes a perfect sharp "V" at zero, smooth and connected everywhere, so it is continuous. But at that tip, it cannot decide on one clear tangent line, left and right slopes clash, so it fails to be differentiable there.
It reminds me of weaving our *thara* patterns—the bamboo strips run continuous, but where they turn sharply at a design’s corner, my fingers must choose a new angle entirely, no single smooth motion suffices. My latest photo shows that saano struggle in the weave’s geometry.
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