Calculus I · Derivative applications, optimization, and related rates
Relate an expanding radius to an area rate
Problem
A circular oil slick remains circular while its radius increases at $0.20$ m/min. At the instant when its radius is $5$ m, how fast is its area increasing? Include units and explain why substituting $r=5$ before differentiating $A=\pi r^2$ would be invalid.
Hint
Name the mathematical object that changes or is sought, and record the domain before doing algebra or calculus.
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