Chapter 11.4, Problem 89E

Existing Home Sales The following graph shows the approximate value of home prices and existing home sales in 2006–2010 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: $P\left(t\right)=t^2-10t+41\left(0\le t\le 4\right)$

Existing home sales: $S\left(t\right)=1.5t^2-11t\left(0\le t\le 4\right),$ where t is time in years since the start of 2006. 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.]