Analyzing problems involving rates of change in applied contexts
At seconds, the tank is being filled at a rate of liter per second.
Lindsay is walking home from school. Her distance from school, in meters, after minutes is modeled by the differentiable function .
Common mistake: Forgetting to include units, or using incorrect units
Another common mistake: Using phrases that refer to “over an interval of time” rather than “at a point in time”
Solving problems that involve instantaneous rate of change
Carlos has taken an initial dose of a prescription medication. The amount of medication, in milligrams, in Carlos's bloodstream after hours is given by the following function:
What is the instantaneous rate of change of the remaining amount of medication after hour?