Answer to Question #273590 in Calculus for Yobro

Question #273590

Poiseuille’s law asserts that the speed of blood that is r centimeters from the central axis of an artery of radius R is S(r) = c(R^2 − r^2), where c is a positive constant. Where is the speed of the blood greatest?


1
Expert's answer
2021-12-01T11:34:39-0500
"S(r) = c(R^2 \u2212 r^2), 0\\leq r\\leq R"

Find the first derivative with respect to "r"


"S'(r)=(c(R^2 \u2212 r^2))'=-2cr"

Find the critical number(s)


"S'(r)=0=>-2cr=0=>r=0"

"S(0)=c(R^2-0)=cR^2>0"

"S(R)=c(R^2-R^2)=0"

The speed of the blood is absolute maximum with value of "cR^2" when "r=0"

(on the central axis).


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