2. (A) The body mass index (BMI) for an adult human is given by the function B(w,h) = where w is the weight measured in kilograms and h is the height measured in meters. (a) Find the linear approximation of the BMI, B, when weight is w = 72 kgs and height is h = 1.50 m2 and then use it to approximate the BMI, B, for an adult human that weighs 73.8 kgs and has a height of 1.53 m. (b) Use differentials to approximate the change in the BMI when weight increases from 72 to 73.8 kg and height increases from 1.50 to 1.53 meters. First show the expression for the total differential dB. (c) which produces a greater percentage change in the BMI, a 1% change in the weight (at a constant height) or a 1% change in the height (at a constant weight)? Explain carefully. Hint: compute the approximate relative change first. (d) Compute the approximate percent change in BMI if the weight increases by 3% and the height increases by 1%. 2. (A) The body mass index (BMI) for an adult human is given by the function B(w,h) = where w is the weight measured in kilograms and h is the height measured in meters. (a) Find the linear approximation of the BMI, B, when weight is w = 72 kgs and height is h = 1.50 m2 and then use it to approximate the BMI, B, for an adult human that weighs 73.8 kgs and has a height of 1.53 m. (b) Use differentials to approximate the change in the BMI when weight increases from 72 to 73.8 kg and height increases from 1.50 to 1.53 meters. First show the expression for the total differential dB. (c) which produces a greater percentage change in the BMI, a 1% change in the weight (at a constant height) or a 1% change in the height (at a constant weight)? Explain carefully. Hint: compute the approximate relative change first. (d) Compute the approximate percent change in BMI if the weight increases by 3% and the height increases by 1%