Optimization Problems

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:
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