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Derivative by definition



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How do you find slope if you only know 1 point ???

In the prior lesson on "what is a derivative", we spent a lot of time trying to understand the difference between a secant and a tangent and, at the end, we learned that a derivative is the slope of a line at a specific point. However, there is a major problem here:

A Specific Example of our dilemna

Imagine that we have some curve, like the red one below, and we know that the point (1,2) is on that curve. The slope of the purple line is the derivative so all that we need to know is the slope of the purple line.

But how do we find the slope of a line when we only know 1 point ?
$slope = \frac{\Delta y}{\Delta x} = \frac{2 - \color{red}{?} }{1 - \color{red}{?} } $
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