   Chapter 14.3, Problem 91E

Chapter
Section
Textbook Problem

A model for the surface area of a human body is given by the functionS = f(w, h) = 0.1091w0.425t0.725where 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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