Unit 4 · 4 lessons
Applications of Derivatives
Put the derivative to work: velocity and acceleration of moving objects, instantaneous rates in population, decay, temperature, daylight, tides and prices, and optimization problems that find the biggest box, the cheapest can and the fare that earns the most.
- 42 practice questions
- 31 flashcards
- 3 interactive lessons
Lessons
- 1Motion: Displacement, Velocity and AccelerationVelocity is the derivative of position and acceleration is the derivative of velocity. The signs of v and a tell you when an object is at rest, when it turns around, and whether it is speeding up or slowing down.Interactive10 questions
- 2Rates of Change in ContextGiven a model for a population, a decaying sample, a cooling drink, hours of daylight, a tide or a price index, the derivative gives the instantaneous rate of change. The skill is computing it with the right rule and then saying what it means, with units.10 questions
- 3Optimization ProblemsOptimization means finding the largest or smallest possible value of a quantity, such as the biggest box or the can that uses the least metal. Model the quantity as a function of one variable, use the context to fix the domain, then let the derivative find the best value.Interactive11 questions
- 4Optimization in Business and ScienceThe same calculus finds the ticket price that earns the most, the bus fare that maximizes revenue under an exponential demand model, the production level with the lowest cost per item, and how long a foraging bird should stay in a berry patch. Then you interpret the result, with units and a domain check.Interactive11 questions