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: We already more or less do this on p65 and p78. See also 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.

MB: 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. YB: I’m not sure how to do 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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