1. Warm-ups
1) Find the equations of all lines tangent to y = 9 – x2 that passes through the point (1, 12).

2. Warm-ups
2) TRUE OR FALSE: If the graph of a function has a tangent line at x = a, then the graph also has a normal line at x = a. Justify your answer.

3. Warm-ups
MULTIPLE CHOICE: Find the average rate of change of f(x) = x2 + x over the interval [1, 3]
A) B) 1/5
C) ¼ D) 4
E) 5

4. Warm-ups
4) MULTIPLE CHOICE: Which of the following is an equation of the normal to the graph of f(x) = 2/x at x = 1.
A) y = ½x + 3/2 B) y = - ½x
C) y = ½x D) y = -½ x + 2
E) y = 2x + 5

5. Rates of change and
Tangent lines:
Applications

6. Example: Using the function f(t) = 2t2 - 1, find the following …
a) The instantaneous rate of change at t = 2.

7. Example:
Using the function f(t) = 2t2 - 1, find the following …

8. Example:
Find the speed of the rock that freefalls from a cliff at t = 1 sec.