1. CHAPTER 2 2.4 Continuity Optimization Problems

2. Steps in Solving Optimizing Problems : 1.Understand the problem. 2.Draw a diagram. 3.Introduce notation. 4.Express notation. 5.Find the relationship of the variables of the function expressed from the notation. 6. Find the absolute maximum and minimum value for the function.

3. CHAPTER 2 2.4 Continuity Example A box with a square base and open top must have a volume of 32,000cm 3. Find the dimensions of the box that minimize the amount of material used.

4. CHAPTER 2 2.4 Continuity First Derivative Test for Absolute Maximum or Minimum Values Suppose that c is a critical number of a continuous function f defined on an interval. a)If f ‘(x) > 0 for all x c, then f (c) is the absolute maximum value of f. b)If f ‘(x) 0 for all x > c, then f (c) is the absolute minimum value of f.

5. Example Find the points on the hyperbola y 2 - x 2 = 4 that are closest to the point (2,0).