The Centers for Disease Control and Prevention provides information on the body mass ind...

The Centers for Disease Control and Prevention provides information on the body mass index (BMI) to give a more meaningful assessment of a person’s weight. The BMI is given by the formula

where w is an individual’s mass in kilograms and h the person’s height in centimeters. While monitoring a child’s growth, you estimate that at the time he turned 10 years old, his height showed a growth rate of 0.6 cm per month. At the same time, his mass showed a growth rate of 0.4 kg per month. Suppose that he was 140 cm tall and weighed 33 kg on his tenth birthday.

(a) At what rate is his BMI changing on his tenth birthday?

(b) The BMI of a typical 10-year-old male increases at an average rate of 0.04 BMI points per month. Should you be concerned about the child’s weight gain?