Unit 1 - Objective 3 - The Derivative



Let's use a previous example: Find f ' (x) for f (x) = x² + 1

The slope of the tangent line to any point on the curve:




The slope of the tangent line at a specific point:

At the point (2,5)

[1st derivative evaluated at the point (2,5)]

The slope of the tangent line at the point (2,5) is 4.


Note 1: The derivative can also be interpreted as:


Note 2: A linear function, y = mx + b, whose graph is a line, is it's own tangent line. So the slope of the tangent line = slope of the line = m.



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