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# Derivatives

# 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?