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Handout Wednesday 9/10
A few left over examples of interpretation of the derivative:
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\(V(m)\) gives the value of a car (in dollars) after the car has been driven \(m\) miles. What does \(V'(m)\) tell us?
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\(C(s)\) measures the rate at which a person burns calories (in calories per hour) when riding a bike at speed of \(s\) kilometers per hour. What does \(C'(19) = 52.1\) mean?
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Your car’s fuel efficiency depends on the speed you drive. Let \(f(s)\) be the fuel efficiency (in miles per gallon) when you are driving at speed \(s\) (in miles per hour). What are the units of \(f'(s)\text{?}\)
Okay, one more: your speed is also a function of time. What happens when you accelerate? Your speed increases! We can ask for the rate at which your speed (which is already a rate of change) changes. We are taking the derivative of a derivative. We call this the second derivative and write \(f''(x)\text{.}\)
Explore this idea by completing the Distance, Velocity, Acceleration! activity
