Calculus I · 2B · review
Higher Derivatives and Motion Review
Review higher derivatives and motion review with mixed practice and links back to the exact lessons behind each skill.
Section overview
Interpretation, motion, and ratesWhat this section is building
Review higher derivatives and motion review with mixed practice and links back to the exact lessons behind each skill.
Position, velocity, and acceleration are synchronized views: amount, rate of amount, and rate of the rate.
Separate direction from speed, and compare the signs of velocity and acceleration before describing speeding behavior.
Treating negative velocity as slowing down or confusing a function's height with the slope of its graph.
Review
Velocity gives direction; speed is . Speed increases when and share a sign. The second derivative measures the change of the first derivative and controls concavity.
For , find , , and all rest times.
Exercise 1 answer
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For on , determine direction changes.
Exercise 2 answer
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Determine speeding-up intervals for the previous problem.
Exercise 3 answer
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Sketch a position graph whose velocity is positive but decreasing.
Exercise 4 answer
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A company's revenue has and . Interpret both values.
Exercise 5 answer
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Estimate and from a table of your own design and explain the needed spacing.
Exercise 6 answer
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Match plausible graphs of , , and for a cubic with two turning points.
Exercise 7 answer
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