Explanation Given information: The oxygen supply, S, in the blood depends on the haematocrit, H, the percentage of red blood cells in the blood: S = a H e − b H Where a and bare positive constants. Fact used: If f ' changes from negative to positive at p, then f has a local minimum at p. f ' changes from positive to negative at p, then f has a local maximum at p. Calculation: S = a H e − b H (Given) Differentiating with respect to ‘H’, we get S ' = a [ e − b H + H e − b H ( − b ) ] = a e − b H − a b H e − b H To find the critical points of S, set S ' = 0 ⇒ a e − b H − a b H e − b H = 0 ⇒ a e − b H ( 1 − b H < To determine (b) To explain: By increasing the values of a andb change the maximum value of S.

6th Edition

ISBN: 9781119399322

Author: Hughes-Hallett

Publisher: WILEY

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Question

Chapter 4.3, Problem 56P

To determine

(a)

To find:

The value of H which maximizes the oxygen supply and the maximum oxygen supply.

To determine

(b)

To explain:

By increasing the values of a andb change the maximum value of S.

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Chapter 4.3, Problem 55P

Chapter 4.3, Problem 57P

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Chapter 4 Solutions

APPLIED CALCULUS (WILEY PLUS)

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(a) To find: The value of H which maximizes the oxygen supply and the maximum oxygen supply.

Solution Summary: The author explains that the oxygen supply in the blood depends on the haematocrit, H, the percentage of red blood cells.