Assertion and reason: rates of change

Exercise and reference answers

Questions

1. Reason

   The chain rule lets the parameter t cancel between the two rates.

   Verdict

   Both are true; the reason explains the assertion.

   Assertion

   dy/dx can be found from dy/dt and dx/dt.

2. Reason

   dx/dt appears in the denominator.

   Verdict

   Both are true; the reason explains the assertion.

   Assertion

   The related-rates formula needs dx/dt ≠ 0.

3. Reason

   A derivative is defined as a limit.

   Verdict

   Both are true; the reason does not explain the assertion.

   Assertion

   f ′(x₀) is the rate of change at a single point.

Explanation