advertisement

Recall!! Optimization Problems (Involving e) Optimizing means determining the values of the independent variable so that the values of a function that models a situation can be minimized or maximized. Algorithm for Extreme Values: If a function f(x) has a derivative at each point on the closed interval, [a,b] calculate f(x) at: 1. 2. all points in the interval [a,b], where f ‘(x) = 0; the endpoints x = a and x = b. The (absolute) maximum value of f(x) on the closed interval [a,b] is the largest of these values, and the (absolute) minimum value of f(x) on the interval is the smallest of these values. Example A drug is injected into the body in such a way that the concentration, C, in the blood at time t hours is given by the function C(t ) 10(e 2t e 3t ) . Determine the time at which the drug has its highest concentration within the first 5 hours. Homework: p.245 #2a, 4a, 5, 6