Project 1 Lecture Notes

Table of Contents• Graphing Functions & Trend Lines

• Demand, Revenue, Cost, and Profit

• Differentiation

• Integration

• Using Solver

Assignment• Read course PowerPoint file:

MBD 2 Proj1.pptx (Slides 1-20)

Graphing Functions• 2 Methods for graphing used:

− Blank Excel file with equally spaced data points (Plotting Points)

− Using Graphing.xlsm file

Plotting Points• Start with blank Excel file

• Generate 2 columns of data- one column of x-values- one column of function values

Plotting Points• To generate the x-values (in a column)

- Given the interval required

- Given the number of points required

Plotting Points• To generate the x-values

- Subtract one from number of points needed

- Divide interval length by this number

- This is the length of each subinterval

Plotting Points• To generate the x-values

- Starting with left endpoint, increase by width of subinterval

- This gives x-value of next point

- Continue until you reach the right endpoint

Plotting Points• To generate the function values (in a column)

- Type function using an “=”

- Use cell references to replace x

Plotting Points• Graphing the function

- Use XY-scatter

- Use Smoothed Lines Without Markers

- Label graphs whenever appropriate

Plotting Points• Special values and functions

- Type PI()

- e Type EXP()

- Type SQRT()

Plotting Points• Ex. Graph the function on the

interval [0, 5] using a blank Excel file with 501 equally spaced points.

• Soln:

173 xexf

Plotting Points• Graph:

-500

-400

-300

-200

-100

0

100

0 1 2 3 4 5 6

x

f (x )

Plotting Points• Piecewise-defined functions

- Use IF statement=IF(statement, rule 1, rule 2)

- statement is a mathematical test- use rule 1 if the statement is true- use rule 2 if the statement is false

- AND function can be used within IF statementEx. AND(0<=A1,3>=A1) tests if A1 is

between 0 and 3

Plotting Points• Ex. Graph the function

using a blank Excel file with 401 equally spaced points.

411432

2 xxxx

xg

Plotting Points• Creating a “plotting points” graph in Excel

• Insert, Scatter, Smooth lines• Right click on plot area• Left click on select data• Add data and format graph

Plotting Points• Soln:

-10

-5

0

5

10

15

20

-6 -4 -2 0 2 4 6

x

f (x )

Plotting Points• Can graph multiple functions simultaneously

• Ex. Graph the functions

using a blank Excel file with 701 equally spaced points.

700400601.04000202.0

xxxx

xg

0,700on 2000004.0 2 xxf

Plotting Points• Soln:

0

50

100

150

200

250

0 200 400 600 800

f(x)

g(x)

Graphing.xlsm• Graphing utility to plot one function

• No cell references used

• Function is typed using the variable x

• Can use parameters (constants) s, t, u, v, or w

Graphing.xlsm

x f (x ) a b stuvw

31

Formula for f (x )ConstantsDefinition Computation Plot Interval

FUNCTION

0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1x

f (x )

Graphing.xlsm• Ex. Graph the function on the

interval [0, 5] using Graphing.xlsm

• Ex. Use Graphing.xlsm to graph the functions on the interval [-4, 4] using the parameter s = 2, 3, 4, and 5.

173 xexf

sxy

Graphing.xlsm• Ex. Graph the function

Using Graphing.xlsm.

700400601.04000202.0

xxxx

xg