There is a mathematical relationship between an infant’s weight and total body surface area (BSA), given by

A(w) = 4.688w^{0.8168-0.0154 log w,}

where w is the weight (in grams) and A(w)  is the BSA in square centimeters.

(a) Find the BSA for an infant who weighs 4000 g.
(b) Find A′(4000) and interpret your answer.
(c) Use a graphing calculator to graph A(w) on [2000, 10,000] by [0, 6000].