1. Linear approximation Median home prices in Austin

2. Tangent lines often give better linear approximations than secant lines
secant line approximation
1995 to 1996
tangent line approximation
at 1996

3. Recall that we defined M'(t) by averaging the two adjacent secant lines at each data point
For the endpoints 1994 and 2002, there is only one interval to use so no average is taken

4. Use both linear methods to estimate the population in 1997
Secant line method (the old way):
Actual value 112,200
Tangent line method (the new way):
Average of secant slopes from 1995 to 1996 and from 1996 to 1997