MHB Finding Slope of Tangent Line: How-To Guide

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My professor shown us in class how to find the slope but I still don't understand
 

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Find which slope? Surely your professor, when showing how to find slope explained that only straight lines have a single slope. Other curves, including "broken line curves" like this, have different slopes at different points. Here there are three different straight lines, one from (-5, 5) to (-2, 2), another from (-2, 2) to (0, 4), and the third from (0, 4) to (4, 2). What is the slope of each of those?
 

Thread 'What do you think of this new explanation of Zeta function?'

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