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Derivative as a Limit of Slopes

The derivative of the function f at x = a is the slope of the function f at x = a.

What the wha—? We typically find the slope of a line between two points. But what does it mean to find the "slope" of a curvy function that isn't a straight line? And how do we find the "slope" of something if we're only given one point?

These questions are actually answerable, thanks to calculus. We can also thank Fig—ahem, Isaac Newton for figuring this stuff out. Snack break, anyone?

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