Recall from Exercise 47 that the surface area of a person’s body may be measured by the empirical formula S(W, H) = 0.0072W^0.425 H^0.725 where W (kg) and H (cm) are the person’s weight and height, respectively. Currently, a child weighs 34 kg and is 120 cm tall.

a. Compute the partial derivatives S_W (34, 120) and S_H (34, 120), and interpret each as a rate of change.

b. Estimate the change in surface area that results if the child’s height stays constant but her weight increases by 1 kilogram.

Data from Exercise 47

Pediatricians and medical researchers sometimes use the following empirical formula* relating the surface area S (m²) of a person to the person’s weight W (kg) and height H (cm):

Find S(15.83, 87.11). Sketch the level curve of S(W, H) that passes through (15.83, 87.11). Sketch several additional level curves of S(W, H). What do these level curves represent?

If Marc weighs 18.37 kg and has surface area 0.648 m², approximately how tall would you expect him to be?

Suppose at some time in her life, Jenny weighs six times as much and is twice as tall as she was at birth. What is the corresponding percentage change in the surface area of her body?

Transcribed Image Text:

S(W, H)= 0.0072 W0.425H0.725