The number of milligrams x of a medication in the bloodstream t hours after a dose is taken can be modeled by x(t) =  4,000t t2 + 16.   (a)For what t-values is x increasing? (b)Find the t-value at which x is maximum (c)Find the maximum value of x

The function A(x) = 0.003x³ -0.04x² +0.16x+0.05 approximates the blood alcohol concentration in a person's bloodstream x hours after drinking 8 ounces of a hard liquor. The function only applies to the interval [0,5]. On what time intervals is the blood alcohol concentration increasing? On what intervals is it decreasing? Determine the interval(s), if any, on which the blood alcohol concentration is increasing. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The blood alcohol concentration is increasing on the time interval(s) (Type your answer in interval notation. Use integers or decimals for any numbers in the expression. Round to the nearest hundredth as needed. Use a comma to separate answers as needed.) B. The blood alcohol concentration is never increasing.