Radius where a circle's area and perimeter grow equally

Question

A circle's radius starts at $0$ and grows at a constant positive rate. At what radius are its area and its circumference increasing at the same rate?

Short answer

$r=1$ . $A'=2\pi rr'$ and $C'=2\pi r'$ ; equating them with $r'>0$ gives $r=1$ .

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Lessons behind this question

The Derivative as a Limit: Rates of Change and the Derivative Function
Transforms and Moment Generating Functions
The Chain Rule

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