Learning Outcomes
- Understand the derivative of a function is the instantaneous rate of change of a function.
- Apply rates of change to displacement, velocity, and acceleration of an object moving along a straight line.
Textbook
- Chapter 3.4 Derivatives as Rates of Change
Textbook Assignment
- p. 273: 153, 155, 156, 157
WeBWorK Assginment
- Derivatives-Rates of Change
Exit problems of the session
- A ball is thrown downward with a speed of 8ft/s from the top of a 64-foot-tall building. After t second, its height above the ground is given by $s(t)=-16t^2-8t+64$.
(a). Find the velocity and acceleration functions.
(b). Determine how long it takes for the ball to hit the ground.
(c). Determine the velocity of the ball when it hits the ground.
Key Concepts
- The rate of change of position is velocity, and the rate of change of velocity is acceleration. Speed is the absolute value, or magnitude, of velocity.
Videos and Practice Problems of Selected Topics
- $\rhd$ Interpreting the meaning of the derivative in context. (4:52)
a) Eddie drove from NYC to Philadelphia. The function $D$ gives the total distance Eddie has driven (in kilometers) $t$ hours later he left. What is the best interpretation for the following statement? $D'(2)=100$.
b) The tank is being drained of water. The function $V$ gives the volume of liquid in the tank, in liters, after $t$ minutes. What is the best interpretation for the following statement? The slope of the tangent line to the graph of $V$ at $t=7$ is equal to $-7$. (Optional)
2. * Practice: Analyzing problems involving rates of change in applied contexts. (2 problems with a guiding text). (Optional)
3. * Practice: Interpreting the meaning of the derivative in context. (4 problems) (Optional)
