James Stewart

ISBN: 9781305266643

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.

To determine

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

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)(m−23)+Bh(23,1.10)(h−1.1) (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

To determine

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

Check out a sample textbook solution.

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