Calculus I · 2B · review
Related Rates Review
Review related rates review with mixed practice and links back to the exact lessons behind each skill.
Section overview
Related ratesWhat this section is building
Review related rates review with mixed practice and links back to the exact lessons behind each skill.
The picture supplies a constraint; implicit differentiation transmits known rates through that constraint to the unknown rate.
Draw and label first, write one relationship, differentiate with time, then substitute the snapshot measurements and rates.
Substituting numerical dimensions before differentiating and thereby erasing the very change the problem asks about.
Related Rates Review
Define variables as functions of time, write a relation, differentiate before inserting values, preserve rate signs and units, and interpret the result in words. Similar triangles are often used to eliminate an extra geometric variable.
An oil slick remains circular and area grows at m/min. Find at .
Exercise 1 answer
Write a real attempt before opening the supplied answer.
A cube's volume grows at cm/s. Find when .
Exercise 2 answer
Write a real attempt before opening the supplied answer.
Sand forms a cone whose height always equals its radius. If volume grows at m/min, find height rate at .
Exercise 3 answer
Write a real attempt before opening the supplied answer.
A spotlight tracks a plane at constant altitude. Derive an angle-rate formula.
Exercise 4 answer
Write a real attempt before opening the supplied answer.
Explain why substituting into before differentiating destroys the related-rate information.
Exercise 5 answer
Write a real attempt before opening the supplied answer.
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