Day 13, Mat128: Calculus A

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Next time:

Today:

Announcements
- Friday's quiz will cover section 1.4: the derivative as a function.
- Your exam corrections are also due on Friday.
- No new assignment. Please continue working on section 1.5 for Friday.
Last time we just about finished with section 1.4: I want to say a little more about our worksheet for Section 1.4, using my doctored up version.
1. Review the derivative of \(f(x)=\frac{1}{x+1}\)
2. Finish off the graph of the derivative at the end of the worksheet.
Today we cover Section 1.5, and get started on the 1.5 worksheet.
- Let's start, however, with one more "tricky" derivative calculation, of the function \[ f(x)=\sqrt{x} \] At this point, we're using the limit definition (which you all can write down in your sleep): \[ f'(x) = \lim_{h \to 0} \frac{f(x+h)-f(x)}{h} \]
- Now a look over the preview exercise: where is it leading us?
  I would say that the author is trying to hammer home the notion that average and instanteous velocities are related, and are related to slopes of lines.
  At times the instantaneous rate of change is the average rate of change (for example, when you are moving at a constant rate of speed over a stretch of highway).
  Finally, the importance of units -- of knowing how to interpret the rates of change.
- Furthermore, as I harped on in section 1.4, the author attempts to convince you that the best way to handle instantaneous rate of change estimates is via the centered difference formula (as in Activity 1.5.2).
  The most important part of that is part d. Let's take a look at that. In this part, we're really using the derivative to gather some important information.... (Well, "important" if you like baked potatoes, and want them cooked just so!:)
- Let's take a look at your 1.5 worksheet. In particular, let's take a look at problem 3. Please work on these for Friday.
Links:
- Exam 1

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