Section 14.4

The Tangent Problem;

The Derivative

OBJECTIVE 1

Find an equation of the tangent line to the graph of f(x) = 2x2 at the point (1, 2).

OBJECTIVE 2

2Find the derivative of 3 2 1 at 1. That is, find 2 .f x x x f

2

Use a graphing utility to find the derivative of

3 2 1 at 1. That is, find 2 .f x x x f

3

OBJECTIVE 3

8

OBJECTIVE 4

where t is the elapsed time that the ball is in the air. The ball misses the rooftop on its way down and eventually strikes the ground.

(a) When does the ball strike the ground?(b) At what time t will the ball pass the rooftop on its way down?(c) What is the average speed of the ball from t = 0 to t = 2?(d) What is the instantaneous speed of the ball at time t?(e) What is the instantaneous speed of the ball at t = 2?(f) When is the instantaneous speed of the ball equal to zero?(g) What is the instantaneous speed of the as it passes the rooftop on the way down?(h) What is the instantaneous speed of the ball when it strikes the ground?