The body mass index (BMI) is a number that can be calculated for any individual as follows: Multiply a person’s weight by 703 and divide by the person’s height squared. That is,

where w is in pounds and h is in inches. The National Heart, Lung, and Blood Institute uses the BMI to determine whether a person is “overweight” (25 ≤ BMI < 30) or “obese” (BMI ≥ 30).

(a) Calculate the BMI for Lebron James, basketball player for the Los Angeles Lakers who is 250 lb. and 6′8′′tall.    
(b) How much weight would Lebron James have to lose until he reaches a BMI of 24.9 and is no longer “overweight”? Comment on whether BMI cutoffs are appropriate for athletes with considerable muscle mass.

(c) For a 125-lb female, what is the rate of change of BMI with respect to height?
(d) Calculate and interpret the meaning of ƒ′(65).
(e) Use the TABLE feature on your graphing calculator to construct a table for BMI for various weights and heights.
(f) Using the fact that 1 in. = 0.0254 m and 1 lb = 0.4536 kg, transform this formula to handle metric units.

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BMI = 703w h²