Find the absolute maximum and minimum values of f on the given interval. f(x) =

Question

Find the absolute maximum and minimum values of f on the given interval. f(x) = x + 1/x, {0, 2, 4} absolute minimum value 2 absolute maximum value 17/4 After the consumption of an alcoholic beverage, the concentration of alcohol in the bloodstream (blood alcohol concentration, or BAC) surges as the alcohol is absorbed, followed by a gradual decline as the alcohol metabolized. The function C(t) = 1.350e^-2.802t models the average BAC, measured in mg/mL, of a group of eight male subjects t hours after rapid consumption of 15 mL of ethanol (corresponding to one alcohol drink). What is the maximum average BAC during the first 5 hours? ________ mg/mL. When does it occur? ______h

Explanation / Answer

C’(t) = 1.35*e^(-2.802*t) + 1.35*t* e^(-2.802*t)*(-2.802) = 1.35* e^(-2.802*t)*(1 – 2.802*t)

Because e^(-2.802*t) > 0,

C’(t) = 0 ======> 1.35* e^(-2.802*t)*(1 – 2.802*t) = 0 ======> (1 – 2.802*t) = 0 =====> t = 1/2.802

C(1/2.802) = 1.35*(1/2.802)*e^(-2.802/2.802) = 1.35*(1/2.802)*e^-1 = 0.1772

C(0) = 1.35*0*e^0 = 0

C(5) = 1.35*5*e^(-2.802*5) = 5.56*10^-6

Therefore the maximum BAC is 0.1772 mg/mL, and it occurs 1/2.802 0.3569 hours after the consumption.

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