Practice question · Multiple choice
Velocity, marginal cost and population growth rate are all derivatives. Why does one mathematical operation describe such unrelated quantities?
Hints
- Write each of the three as "the rate of change of ___ with respect to ___".
- Ask what is left when you strip out the subject matter.
Show the answer
D. Because all three ask how fast one thing changes as another does.
Why
Write the three out and one question remains once the nouns are stripped: how fast does this change as that changes. It is the same abstraction argument as the vector-space lesson, prove it once and every field gets its results free. Marginal cost is not an economic idea borrowed from physics; it is the same derivative asked about a different pair of variables.
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