Solved: In Exercises 1723, use derivatives to identify local maximaand minima and points

Chapter 4, Problem 23

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In Exercises 1723, use derivatives to identify local maximaand minima and points of inflection. Graph the function.When you cough, your windpipe contracts. The speed,v(r), with which you expel air depends on the radius, r,of your windpipe. If a is the normal (rest) radius of yourwindpipe, then for 0 r a, the speed is given by:v(r) = k(a r)r2 where k is a positive constant.What value of r maximizes the speed? For what value isthe speed minimized?

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