Answer to Question #272447 in Calculus for Hamda

Question

Poiseuille’s law asserts that the speed of blood that is �џ centimeters from the central axis of an artery of radius �х is �ц(�џ)=�ѐ(�х2−�џ2), where �ѐ is a positive constant. Where is the speed of the blood greatest?

Answer 1

speed of blood that is r centimeters from the central axis of an artery of radius R:

$S(r)=c(R^2-r^2)$

where c is a positive constant

for maximal speed:

$S'(r)=-2cr=0$

$r=0$

so, speed of the blood is greatest on the central axis of an artery