Cartoon Calculus: Ch 7 (The calculus toolkit)

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 83: (Introductory page)

Pages 84-85: Some fruits are easy to eat… // What you need are the right tools.

MB: explain why this particular function? And if the variable should be time, as I suspect, then make it t, not x, which is distance in this text. YB: It’s just an example, I think it’s okay as-is.

Pages 86-87: Let’s start with the sum rule… // The sum rule also makes sense…

Pages 88-89: Next, let’s look at the constant multiple rule… // The constant multiple rule also makes sense…

MB: p88: State that you will use the letter ‘c’ for a constant, or number, that does not change. YB: Will ponder, either for here or for page 85.

Pages 90-91: Somewhat more complicated is the product rule… // As x changes…

WM: Page 91 – very nice. YB: Thanks!

Pages 92-93: There are lots of other rules… // Luckily, we’ve already completed step 1…

MB: p92: I am not sure that in this text you need such a long derivation. YB: Well, part of the point here is to try to explain induction for readers who haven’t seen it.

WM: Page 93 – maybe move the “it may help” statement down in the picture to that third step where you actually use it. YB: No, we need them here. What we showed on page 79 is that d/dx[x]=1, and what we need here is to show that d/dx[x^1]=x^0. Connecting those requires knowing that x^1=x and that x^0=1.

Page 94: Thanks to the calculus toolkit…

MB: p. 94 Misprint in top equation. YB: Good catch, and this has been fixed in the latest draft.

Perhaps tell us what you are doing in terms of distance, velocity, etc., before you do it. The whole discussion, p. 94-97, should be accompanied by a picture of the trajectory and an explanation of what the various functions and derivatives are on this picture.

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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