Chapter 11.4, Problem 90E

Existing Home Sales Leading to the Financial Crisis The following graph shows the approximate value of home prices and existing home sales in 2004–2007 (the 3 years prior to the 2008 economic crisis) as a percentage change from 2003, together with quadratic approximations:

Home prices and sales of existing homes

The quadratic approximations are given by

Home prices: $P\left(t\right)=6t^2-27t+10\left(0\le t\le 3\right)$

Existing home sales: $S\left(t\right)=-4t^2+4t+11\left(0\le t\le 3\right),$ where t is time in years since the start of 2004. Use the chain rule to estimate ${\frac{dS}{dP}|}_{t=2}$. What does the answer tell you about home sales and prices? [HINT: See Quick Examples 6 and 7.]