1. 32 – Applications of the Derivative No Calculator
Derivative Investigations
32 – Applications of the Derivative No Calculator

2. Equation of tangent line to f(x) at x = a:
Slope of a normal line to f(x) at x = a:
1. Find the equation of the line tangent to f(x) at x = 1.
2. Find the equation of the line normal to f(x) at x = 2.

3. 3. Find the equation of the line tangent to g(x) at x = 2.
4. Find the equation of the line normal to g(x) at x = –1.

4. 5. Find the equation of the line tangent to h(x) at x = 0.
6. Find the equation of the line normal to h(x) at x = 1.

5. DERIVATIVE
POSITION s(t)
VELOCITY v(t)
ACCELERATION a(t)
SLOPE
AREA X

6. A ball is thrown straight down from the top of a 100 foot tall building with an initial
velocity of
Use the position function for free-falling objects:
7. Determine the position function of the ball.
8. Find v(2). Include units in your answer.
9. Find a(3). Include units in your answer.

7. Given
10. Find the initial position.
11. Find the initial velocity.
12. Find the average velocity on the interval [0, 2].
13. Find a(1).

8. Given
14. Find a(1).
15. Find the average acceleration on the interval [0, 3].

9. Given
16. Find the average velocity on [0, 2].
17. Find the velocity at t = 2.
18. Find the average acceleration on [0, 2].
19. Find the acceleration at t = 2.