   Chapter 10.2, Problem 36E ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

#### Solutions

Chapter
Section ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

# Poiscuille's law—velocity of blood According to Poi- seuille’s law, the speed S of blood through an artery of radius r at a distance x from the artery wall is given by S = k [ r 2 − ( r − x ) 2 ] where k is a constant. Find the distance x that maximizes the speed.

To determine

To calculate: The distance that maximizes the speed where the speed S of blood through an artery of radius r at a distance x from the artery wall is given by S=k[r2(rx)2].

Explanation

Given Information:

The provided function is S=k[r2(rx)2].

Formula used:

To find relative maxima and minima of a function,

1. Set the first derivative of the function to zero, f'(x)=0, to find the critical values of the function.

2. Substitute the critical values into f(x) and calculate the critical points.

3. Evaluate f(x) at each critical value for which f(x)=0.

(a) If f(x0)<0, a relative maximum occurs at x0.

(b) If f(x0)>0, a relative minimum occurs at x0.

(c) If f(x0)=0 or f(x0) is undefined, the second derivative test fails and then use the first derivative test.

Calculation:

Consider the function S=k[r2(rx)2].

Simplify the function

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