the drop in blood pressure of a typical patient who is given a certain medication is given by F(x)=0.028x^2(19-x) where x is the amount of medication in cubic centimeters. What is the maximum drop in blood pressure for this patient?

Answer 1

could use the product rule, but in this case I would expand
f(x) = .532x^2 - .028x^3
f'(x) = 1.064x - .084x^2
= 0 for a max/min

x(1.064 - .084x) = 0
x = 0, which will produce the min
or
x = 1.064/.084 = 12 2/3 = 38/3

f(38/3) = .... button - pushing time

(I got appr 28.45)