CHAPTER 2 2.4 Continuity Optimization Problems. Steps in Solving Optimizing Problems : 1.Understand the problem. 2.Draw a diagram. 3.Introduce notation.

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Presentation transcript:

CHAPTER Continuity Optimization Problems

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.

CHAPTER 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.

CHAPTER 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.

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