1. Tuesday, October 24 Lesson 3.1 Score 2.8
“When you have exhausted all possibilities, remember this ~ YOU HAVEN’T.” Thomas Edison
Lesson 3.1
The formal definition of the derivative
Score 2.8

2. 3.1 The Derivative of a function

3. Review: Secant line versus Tangent line
The slope of the tangent line at x = a is called the Derivative of the function f ’(a).
“ f prime at a”

4. When the limit exists, we say that
the function is differentiable at a.
As point Q gets closer to point P, then h gets closer to zero.

5. As point Q gets closer to point P, then x gets closer to a.

7. The equation of a line: 𝑦− 𝑦 1 =𝑚(𝑥− 𝑥 1 )
The equation of a line tangent
to a curve at the point (a, f (a) ): 𝑦−𝑓 𝑎 = 𝑓 ′ 𝑎 𝑥−𝑎
Or 𝑦=𝑓 𝑎 +𝑓′(𝑎)(𝑥−𝑎)

9. Lesson 3.1 Scoring Guidelines5
Limit done both ways 7
Slope of secant; is it larger or smaller than f’(2)? 9
Estimate f’(1) and f’(2) 13
Which is larger? 19
Find derivative; then write equation of tangent line 35
Find derivative using limit process 49
Intervals on which derivative is positive 51
Find f(x) and a 56 59
A B.