Practice question · Multiple choice
A cyclist's speed is falling and their acceleration is negative, but a news report says the rate of decrease is slowing. Which derivative is that, and what is happening?
Hints
- 'Speed falling' is one derivative. 'The fall easing' is a statement about that derivative.
- Ask what the sign and direction of the second derivative must be.
Show the answer
D. The second derivative, since acceleration is easing toward zero
Why
Acceleration is negative and heading toward zero, so the second derivative is positive: braking that is easing off. Nested rate-of-change language is exactly where intuition fails, and it is the same structure as the epidemic reported as 'cases still rising, but more slowly', which is a claim about the second derivative.
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