1. 2.1A Tangent Lines & Derivatives

2. Tangent Line: a line that intersects a curve at a point P & whose slope approximates the behavior of the curve at or very close to point P. Slope = Instantaneous Rate of Change at P

3. Secant Line: a line that intersects a curve at two points, P & Q
Secant Line: a line that intersects a curve at two points, P & Q. Slope = Average Rate of Change between P & Q

5. P = (a, f(a)) with a slope of,
Tangent Line to f (x)
The line through
P = (a, f(a)) with a slope of,

6. Ex 1: Find the slope of the tangent line at x = 3

7. Derivatives
The derivative of f is:

8. Ex 2: Find f (x) and use it to find the equation of the tangent line to f (x) at x = 1.

9. 2.1A pg. 103 # 1, 3, 4, # 9 – 33 EOO, # 71, & 77 (use slope limit for 9,71 & 77)

10. Ex 3: Find the slopes of the tangent lines to the graph at (0, 1) and (−1, 2).