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Multivariable Calculus

8th Edition
James Stewart
ISBN: 9781305266643

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Multivariable Calculus

8th Edition
James Stewart
ISBN: 9781305266643
Textbook Problem

A model for the surface area of a human body is given by the function

S = f(w, h) = 0.1091w0.425t0.725

where w is the weight (in pounds), h is the height (in inches), and S is measured in square feet. Calculate and interpret the partial derivatives.

(a) S w ( 160 , 70 )

(b) S h ( 160 , 70 )

(a)

To determine

To find: The value of Sw(160,70) using the given function S=f(w,h)=0.1091w0.425h0.725 and interpret the result.

Explanation

Given:

The function S=f(w,h)=0.1091w0.425h0.725 , where h is height (in inches), w is weight (in pounds) and S is measured in square feet.

Calculation:

The given function is, S=0.1091w0.425h0.725 .

Take the partial derivative with respect to w and obtain Sw .

Sw=w(0.1091w0.425h0.725)=0.1091h0.725w(w0.425)=0.1091h0.725(0.425)w0.575=0.0464h0.725w0

(b)

To determine

To find: The value of Sh(160,70) using the given function S=f(w,h)=0.1091w0.425h0.725 and interpret it.

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Chapter 14 Solutions

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P-14RECh-14 P-15RECh-14 P-16RECh-14 P-17RECh-14 P-18RECh-14 P-19RECh-14 P-20RECh-14 P-21RECh-14 P-22RECh-14 P-23RECh-14 P-24RECh-14 P-25RECh-14 P-26RECh-14 P-27RECh-14 P-28RECh-14 P-29RECh-14 P-30RECh-14 P-31RECh-14 P-32RECh-14 P-33RECh-14 P-34RECh-14 P-35RECh-14 P-36RECh-14 P-37RECh-14 P-38RECh-14 P-39RECh-14 P-40RECh-14 P-41RECh-14 P-42RECh-14 P-43RECh-14 P-44RECh-14 P-45RECh-14 P-46RECh-14 P-47RECh-14 P-48RECh-14 P-49RECh-14 P-50RECh-14 P-51RECh-14 P-52RECh-14 P-53RECh-14 P-54RECh-14 P-55RECh-14 P-56RECh-14 P-57RECh-14 P-58RECh-14 P-59RECh-14 P-60RECh-14 P-61RECh-14 P-62RECh-14 P-63RECh-14 P-64RECh-14 P-65RECh-14 P-1PCh-14 P-2PCh-14 P-3PCh-14 P-4PCh-14 P-5PCh-14 P-6PCh-14 P-7PCh-14 P-8P

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