1. 2-4 Rates of change & tangent lines

2. Average Rate of Change =
This is the slope of the secant line through 2 points on f (x)
(x1, f (x1)) and (x2, f (x2))
As the intervals get closer together we approach the slope
of a tangent line
Def: Slope of a Curve at a Point
If y = f (x) and P(a, f (a)) is a point on the curve, then
(as long as the limit exists)

3. We can use the definition above to find the equation of the tangent line to the curve. We need two things:
(1) a slope (2) a point
Ex 4) Let
a) Find the slope of the curve at x = a.
b) Where does the slope equal ?

4. Difference Quotient of f at a
Two Notes:
(1) secant slope  its limit is the slope of the curve
& the tangent at x = a
(2) average rate of change  its limit is the function
rate of change at x = a

5. Normal to a Curve
Def: Normal Line: the line  to the tangent at a point
Ex 5) Write an equation for the normal line to the curve
First find slope of tangent:
(tangent)
 = ½
(1, 3)
y – 3 = ½(x – 1)

6. homework
Pg. 84 #6 – 54 (mult of 6)
Pg. 92 #1 – 6, 8 – 9