## SectionC.2From Section 3.2- Comparing Functions and Numeric Derivatives

The spreadsheet skill in this section was to make a table and graph of a function and its derivative. We use a variety of approaches to find numeric derivatives.

### SubsectionC.2.1Derivatives from the Intuitive Approach

We build a worksheet that plotsthe function and a secant curve with control over del x 3.2.5. We then reduce del x until the the graphs appear to be the same the graphs appear to be the same 3.2.6. Screencast of example using this approach. 3.2.3

### SubsectionC.2.2Derivatives from Numerical Limits

Without using graphs, we can also look at the slope of the secant line as del x gets small. 3.2.7. from one row to the next. Screencast of example using this approach. 3.2.3

### SubsectionC.2.3Graphing a Function with its Numeric Derivative

To build a chart of a function and its derivative and to grpah the functions together, we use a variant of the approach from the previous section. We set up successive colummes for x, x+del x, x-del x, f(x), f(x+del x) f(x-del x), and f'(x) 3.2.11. I then only have the enter the formula for the function one time, under f(x). Quick fill then provides the correct formula for f(x+del x) and f(x-del x). Screencast of example using this approach. 3.2.9
In practive, we usually set $$del x= 0.001\text{.}$$

### SubsectionC.2.4Using Trendline to find Derivative Formulas

If the grpah of the numerical deerivative looks like a model we know, and one that trendline will produce, we can try to obtaina formula useing Trendline. Add a trendline and display the formula of the trendline and $$R^2$$ If the model is correct, $$R^2=1\text{.}$$ Screencast of example using this approach. 3.2.14