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:

- the instantaneous rate of change or just rate of change
- the instantaneous velocity or just velocity
- the speed of an object

**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.