   Chapter 14.4, Problem 41E

Chapter
Section
Textbook Problem

In Exercise 14.1.39 and Example 14.3.3, the body mass index of a person was defined as B(m, h) = m/h2, where m is the mass in kilograms and h is the height in meters.(a) What is the linear approximation of B(m, h) for a child with mass 23 kg and height 1.10 m?(b) If the child’s mass increases by 1 kg and height by 3 cm, use the linear approximation to estimate the new BMI. Compare with the actual new BMI.

(a)

To determine

To find: The linear approximation of the body mass index B(m,h)=mh2 at the mass m=23kg and the height h=1.10m .

Explanation

Given:

The body mass index B(m,h)=mh2 .

Where m is mass in kilograms.

The term h is height in meters.

Calculation:

The given function is, B(m,h)=mh2 (1)

The linear approximation of the function B(m,h)=mh2 at (23,1.10) is defined as,

B(23,1.10)B(23,1.10)+Bm(23,1.10)(m23)+Bh(23,1.10)(h1.1) (2)

Find the partial derivative of the equation (1)with respect to m at the point (23,1.10) ,

Bm(m,h)=1h2(1)=1h2Bm(23,1.10)=1(1.1)2=0.8264

Find the partial derivative of the equation (1) with respect to h at the point (23,1.10) ,

Bm(m,h)=m(2h3)=2mh3Bm(23,1

(b)

To determine

To estimate: The linear approximation of the body mass index B(m,h)=mh2 , use it to compare the actual BMI.

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