1. 2.7 Tangents, Velocities, & Rates of Change

2. Curve C has equation y = f(x)
Curve C has equation y = f(x). To calculate the slope of a secant segment
from point P to point Q, we use

3. But what if we want the EXACT slope of the tangent line at point P???
DEFINITION: The tangent line to the curve y = f(x) at the point P (a, f(a))
Is the line through P with slope
Example: Find an equation of the tangent line to the parabola
at the point P (1,1)

4. We can also use the following (similar) equation for slope:
Find an equation of the tangent line to the hyperbola at the point (3,1)

5. Velocity: Average velocity
Instantaneous velocity

8. Read 2.7 p
Work p. 155 #1, 3, 6, 11, 15, 17, 24