Help on Calculus Question

Question

Hello! I need help on this question:

For a dosage of x cubic centimeters (cc) of a certain drug, the resulting blood pressure B is approximated by the function below. Find the maximum blood pressure and the dosage at which it occurs.

B(x)=320x^2 - 3200x^3, 0 <= x <= 0.10

Answer 1

To find the max and/or min, take the derivative and set it equal to zero.

for B(x) = 320x² - 3200x³, the derivative is:

B'(x) = 640x - 9600x²

Setting it equal to zero, we get:

640x - 9600x² = 0

640x(1 - 15x) = 0

x = 0 or x = 1/15 = 0.066667 (and 1/15 is between 0 and 0.1)

Is x = 1/15 a maximum or a minimum? Try x = 1 and x = .01 to find out. B(1) = -2880 and B(0.01) = 0.0288 while f(0.06666667) = 0.47407 therefore x = 1/15 is a maximum and that maximum is B = 0.474

Answer 2

The maximum blood pressure is .4741 and the dosage at which it occurs is .0667.

blood pressure = B(x) x= dosage

the maximum occurs where the derivative of B(x) changes from positive to negative when B(x) is set = 0