Section 14.4: Tangent Planes

In Exercise 14.1.39 and Example 14.3.3, the body mass index of a person was defined as \(B(m, h) = \frac{m}{h^2}\), where \(m\) is the mass in kilograms and \(h\) is the height in meters.

1. What is the linear approximation of \(B(m, h)\) for a child with mass 23 kg and height 1.10 m?

2. 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.