Practice question · Sort into groups
Sort each quantity by whether it is itself the derivative of some other quantity.
Groups: Is a derivative of something else · Is not a derivative
- Position
- Marginal cost
- Acceleration
- Total cost
- Velocity
- The growth rate of a population
Hints
- Ask, for each one, 'the rate of change of WHAT?'
- Two of these are the base quantities that the others are rates of.
Show the answer
Is a derivative of something else: Velocity, Acceleration, Marginal cost, The growth rate of a population
Is not a derivative: Total cost, Position
Why
Velocity is the rate of position, acceleration the rate of velocity, marginal cost the rate of total cost, and the growth rate the rate of population. Position and total cost are the underlying totals, each application pairs a total with its rate, and the derivative is always the bridge.
Practise Applications of Differentiation
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