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Handout Tuesday, 9/2
Today we will start by discussing any questions about the practice problems due tonight. Then some discussion section 1.3 on the derivative at a point. Finally, we will do the first Learning Target Quiz.
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Look at question 2 from last Friday’s activity. We want to evaluate that limit. Notice that it is a very particular type of limit. It is a limit of an average velocity between two points. What are they?
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Look at the preview activity for 1.3. Go over this carefully.
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We will want to evaluate these sorts of limits a bunch. But what does \(\d\frac{f(a+h) - f(a)}{h}\) look like for different functions? Try this out with a bunch of different examples.
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The limit of this difference quotient is called the derivative of \(f\) at \(a\), and written \(f'(a)\text{.}\) Here we are thinking of \(a\) as a specific number. So examples would be \(f'(2)\) or \(f'(0)\text{.}\)
