IB Math SL 2 Magister Lao & Magistra Pak

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3-11: DWBAT use calculus to find optimal solutions. AIM: How do we use derivatives to find maximum or minimum values of functions in context? HW for tonight: Exercise 11.3 #22; Exercise 13.5 #3; Exercise 13.5 #24

Process of Optimization: • Have a function whose min/max you want to find* • Take the derivative of the function • Set 𝑓𝑓 ′ (𝑥𝑥) = 0 and solve • Check whether your solution is a max or a min *The new part of this process for us will be this first step, and it often helps to draw a diagram. To do this, ask yourself two questions: 1. What are we trying to optimize? 2. What is the equation for that, in one variable?

Problem 1 Find two nonnegative numbers whose sum is 9 and so that the product of one number and the square of the other is a maximum.

Problem 2 Mr. Lao has 200 meters of electric fence with which he as many students as possible. What's the maximum area he can enclose?


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Problem 3 Farmer Lao has 2500 meters of electric fence with which he wants to create a rectangular enclosure for chickens. He will use a long, straight river as one side of the fencing for the other three sides (chickens can't swim).


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What's the maximum roaming area he can give the chickens?

Problem 4 Find two positive numbers whose product is 750 and for which the sum of one and 10 times the other is a minimum.

Problem 5 A rectangular box is made by cutting out squares from the corners of a 25 cm by 40 cm rectangle of paper and then folding the paper to form the box. What size squares must be cut out to produce a box that can store the greatest volume?

HW for tonight: Exercise 11.3 #22; Exercise 13.5 #3; Exercise 13.5 #2