SOLUTION: An experiment was set up to find a relationship between weight and systolic blood pressure in children. Using hospital records for 5,000 children, the experimenters found that the

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Question 1088243: An experiment was set up to find a relationship between weight and systolic blood pressure in children. Using hospital records for 5,000 children, the experimenters found that the systolic blood pressure was given approximately by
P(x)=17.5 (1+lnx); 10 < x < 100
where P(x) is measured in millimeters of mercury and x is measured in pounds.
(a) what is the rate of change of blood pressure with respect to weight at the of 40-pound weight level?
(b) Find the weight at which the rate of change of blood pressure with respect to weight is 0.3 millimeter of mercury per pound.
Answer by htmentor(1343) About Me  (Show Source):
You can put this solution on YOUR website!
dP(x)/dx = d/dx(17.5 + 17.5ln(x)) = 17.5/x
(a) dP/dx at x = 40 = 17.5/40 = 0.44
(b) dP/dx = 0.3 = 17.5/x -> x = 17.5/0.3 = 58.33 lbs.