More derivatives

Learning objectives

Interpret second derivatives
Measure change two ways: absolute change and relative (percent) change
Understand relative rates (such as birth rates)
- (percent change in $y$ ) $\approx$ (rel derivative) $\times \Delta x$
- rel derivative $\approx (\ln f(x_2)-\ln(f(x_1))/(x_2-x_1)$
Understand elasticity (such as price elasticity of demand)
- (percent change in $y$ ) $\approx$ (elasticity) $\times$ (percent change in $x$ )
- elasticity $\approx (\ln f(x_2)-\ln f(x_1))/(\ln x_2-\ln x_1)$

Before class

Read Hughes-Hallett 2.3 (relative rate of change), 2.4, 4.6
Ponder problems 2.3. 42, 43, 44, 46; 2.4. 2, 10, 20, 26; 4.6. 1, 2, 3, 4.
Consult the main points of the lesson.
Consult notes on two types of change and three derivatives. Focus on the summary at the end.

.In class

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