Section Week 3 (9/8 - 9/12)
We will cover sections 1.4, 1.5, and start 1.6 this week.
Handout Monday 9/8
We are still working on 1.4 today. Thinking about the derivative as a function of slopes or of instantaneous rates of change. So instead of finding \(f'(a)\text{,}\) we are finding a function \(f'(x)\text{.}\)
Here are two things to try:
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Interesting, we get the equation of a line for the derivative. This line is NOT the tangent line: it is a line that gives slopes of tangent lines at any given point.
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Let’s try the same thing with \(f(x) = x^3 + 1\text{.}\)
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Graphically, what do we guess the derivative function will look like?
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Using the limit definition, find \(f'(x)\text{.}\) We will need to multiply out \((x + h)^3 = x^3 + 3x^2h + 3xh^2 + h^3\text{.}\)
