Approximating Derivatives with Spreadsheets
MAT 135 @ Center Grove High School
Robert Talbert, PhD
MAIN GOAL OF CALCULUS: 
Find the instantaneous rate of change in a function at a single point. 
But what if...
DERIVATIVE OF F(X) AT X = A
Average rate of change from x to a
= Slope of secant line through (a,f(a)) and (x,f(x))
Let second point get arbitrarily close to a
f(x) given as a table, no formulas
ESTIMATION: SYMMETRIC DIFFERENCE QUOTIENTS
MODELING: TRENDLINES USING SPREADSHEET TECHNOLOGY
http://en.wikipedia.org/wiki/Johnson_County,_Indiana
Percentage of Indiana residents
not covered by health insurance
Number of cars sold in the US in 1990 by weight
U.S. Environmental Protection Agency, Automotive Technology and Full Economic Trends Through 1991, EPA/AA/CTAB/91-02, 1991. 
http://www.census.gov/hhes/www/hlthins/historic/index.html
How to find the derivative at a point?
How to compute the derivative function?
Estimate the rate of change in the population
in the year 1950.
What kind of function best models this?
Estimate from symmetric difference quotient: 1060.55 people/yr
Excel demo: Constructing a table for P'(t)
Activity
Hoosier health insurance:  Use symmetric difference quotients to calculate derivative in year 2006. What are the units? What does this mean? Then, make a table for the derivative function. Then, plot the data, fit with appropriate trendline, and calculate derivative. 
Car weights: Same as above. Focus on derivative at 2500. 
Questions?
Contact

Robert Talbert, PhD
Associate Professor of Mathematics and Computing
Franklin College
rtalbert@franklincollege.edu
AIM: rtalbert235
Skype: rtalbert235
Twitter: @RobertTalbert
FC Mathematics and Computing
@fcmathcomp
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