The radius of a circle is increasing. At a certain instant, the rate of increase in the area of the circle is numerically equal to twice the rate of increase in its circumference. What is the radius of the circle at that instant?
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if you let x be your radius, you can find both
the area and the circumference as a function of x.
can you do that ?
Now you want to know what "rate of increase in the area" and "rate of increase in the circumference" is algebraically.
I'm just going to assume that you are reading this.
if you let the Area of the circle "A"
then the rate of increase of A would be A'.
since we are focusing on how fast the area is changing
regarding at what time