Cartoon Calculus: Ch 9 (Optimization)

Quick links to Front matter, Back matter, and:
Part One: Ch 1: Introduction, Ch 2: Speed, Ch 3: Area, Ch 4: Fundamental theorem, Ch 5: Limits
Part Two: Ch 6: Derivatives, Ch 7: Toolkit, Ch 8: Extreme, Ch 9: Optimization, Ch 10: Economics
Part Three: Ch 11: Hard way, Ch 12: Easy way, Ch 13: Revisited, Ch 14: Physics, Ch 15: Conclusion

Page 107: Help

Pages 108-109: Finding extreme values is important in economics… // In this chapter we’re going to use calculus…

Pages 110-111: Our first challenge here is to translate words… // For our problem, it’s easiest to focus…

MB: p.102 etc. Optimization. Emphasize in words that two tendencies (growing height or growing width) fight each other and at optimum they balance. YB: Good suggestion. Maybe we can do this on p111 with text like “But the greater the length is, the smaller the width has to be because we only have 100 feet of fence.” The challenge is going to be trying to say this in as few words as possible and then finding a good place to put those words.

Pages 112-113: It often helps to sketch a graph… // and in this case the graph’s symmetry…

Pages 114-115: In the last chapter we learned… // So we take our function…

WM: Page 115- maybe have someone thinking “L is my variable this time instead of x, but the formulas work in exactly the same way.” YB: Good suggestion, maybe we can put this in the top panel here?

Pages 116-117: Thanks to calculus… // Then all we have to do…

Page 118: The world is full of optimization problems like this…

Quick links to Front matter, Back matter, and:
Part One: Ch 1: Introduction, Ch 2: Speed, Ch 3: Area, Ch 4: Fundamental theorem, Ch 5: Limits
Part Two: Ch 6: Derivatives, Ch 7: Toolkit, Ch 8: Extreme, Ch 9: Optimization, Ch 10: Economics
Part Three: Ch 11: Hard way, Ch 12: Easy way, Ch 13: Revisited, Ch 14: Physics, Ch 15: Conclusion

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