3.7 Optimization.notebook
October 14, 2013
3.7 Optimization
Objective: You will be able to:
• solve applied (real­life) minimum and maximum problems
3.7 Optimization.notebook
October 14, 2013
OPTIMIZATION PROBLEMS
Applied Max and Min Problems
Warm Up: Think about it:
• How can I make a box with largest possible volume from a 8.5 in. by 11 in. piece of paper?
• Why would I?
show alg 2 cut outs
3.7 Optimization.notebook
October 14, 2013
OPTIMIZATION PROBLEMS
Applied Max and Min Problems
1. Make a sketch and label everything
2. Choose a primary equation to optimize
3. Use additional equations to reduce down to one variable
4. Take the derivative to find critical numbers
5. Evaluate each # (critical numbers and endpoints)to find min/max
****pay attention to the domain****
3.7 Optimization.notebook
October 14, 2013
OPTIMIZATION PROBLEMS
Applied Max and Min Problems
Find two non­negative real numbers that add up to 66 such that their product is as large as possible.
• First, think about it! Don't use calculus!
• Find the answer using calculus!
• What other ways could you find the answer?
3.7 Optimization.notebook
October 14, 2013
example 1 p. 218
worked out solution, next slide
3.7 Optimization.notebook
October 14, 2013
3.7 Optimization.notebook
October 14, 2013
Which points on the graph of y = 4 - x2 are
closest to the point (0,2)?
(x,y)
3.7 Optimization.notebook
October 14, 2013
3.7 Optimization.notebook
October 14, 2013
See example 3 p. 220
worked out solution, next slide
3.7 Optimization.notebook
October 14, 2013
3.7 Optimization.notebook
October 14, 2013
A rancher has 400 feet of fencing with which to enclose two adjacent rectangular corrals.What dimensions should be used so that the enclosed area will be maximum? 3.7 Optimization.notebook
October 14, 2013
EXIT
TICKET
Find the length and the width of a rectangle that has a perimeter of 64 feet and a maximum area.
Summary:
Describe a situation where minimizing would be most beneficial. Describe a situation where maximizing would be most beneficial. 3.7 Optimization.notebook
October 14, 2013
3.7 Optimization.notebook
October 14, 2013