5.7 Optimatisation.pptx - MATH 12 5.7 Optimisation What is optimisation Under what situations would we want to \u2018optimise\u2019 Lesson Objective By the

# 5.7 Optimatisation.pptx - MATH 12 5.7 Optimisation What is...

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5.7 Optimisation What is optimisation?Under what situations would we want to ‘optimise’? 10/29/19 MATH 12
Lesson Objective By the end of the lesson, I will be able to… use implicit differentiation to solve optimisation problems
Guidelines for Solving Optimisation Problems (p375) 1.Read and understand the problem.2.Sketch a diagram if possible.3.What quantities are given? Use variables to create an equation, f(x). What quantity needs to be optimized?4.Find f ‘(x). Find the critical numbers.5.Use the first derivative test to find the absolute maximum or minimum of f(x).6.Check to see whether the answer is reasonable. Write a concluding sentence.
Ex1. Mary has 100 m of fencing to fence a rectangular pen. What are the dimensions of the pen that has the largest area?
Ex2. Find two integers whose difference is 16 and whose product as small as possible.
Ex3.Which point(s) on the graph of are closest to point (0, 6) ?
Ex4.A 500 mL cylinder is made of metal. Find the dimensions that will minimize the costof the metal to manufacture the cylinder.
Ex5. Minimum CostAn offshore oil well is 2km off the coast. The refinery is 4km down the coast. Laying pipe in the ocean is twice as expensive as on land. What path should the pipe follow in order to minimize the cost?
Ex6. The volume of a rectangular box will be 15 m3. The box has a square base and top. The material for the base costs \$7.50/m2. The material for the top costs \$2.50/m2 and for the sides costs \$4.50/m2. Find the dimensions that will minimize the cost of materialsfor the box.
Lesson Objective By the end of the lesson, I will be able to… use implicit differentiation to solve optimisation problems
Suggested Practice Page 379 #5-17,21-25,29,49 (odd #s) Vocabulary: Optimisation