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 f x   3e x  17 on the
interval [0, 5] using a blank Excel file with 501
equally spaced points.
• Soln:
Plotting Points
• Graph:
100
0
0
1
2
3
-100
f (x ) -200
-300
-400
-500
x
4
5
6
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 statement
Ex. AND(0<=A1,3>=A1) tests if A1 is
between 0 and 3
Plotting Points
• Ex. Graph the function
2 x  3  4  x  1
g x    2
1 x  4
 x
using a blank Excel file with 401 equally spaced
points.
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:
20
15
10
f (x )
5
0
-6
-4
-2
0
-5
-10
x
2
4
6
Plotting Points
• Can graph multiple functions simultaneously
• Ex. Graph the functions
f x   0.0004 x  200 on 0,700
2
0  x  400
0.2 x  20
g x   
0.1x  60 400  x  700
using a blank Excel file with 701 equally spaced
points.
Plotting Points
• Soln:
250
200
150
f(x)
g(x)
100
50
0
0
200
400
600
800
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
Definition
Formula for f (x )
Computation
f (x )
x
Plot Interval
a
b
FUNCTION
1
0.8
0.6
f (x )
0.4
0.2
0
0
0.2
0.4
0.6
x
0.8
1
Constants
s
t
u
v
w
Graphing.xlsm
• Ex. Graph the function f x   3e x  17 on the
interval [0, 5] using Graphing.xlsm
• Ex. Use Graphing.xlsm to graph the functions
y  x s on the interval [-4, 4] using the parameter
s = 2, 3, 4, and 5.
Graphing.xlsm
• Ex. Graph the function
0  x  400
0.2 x  20
g x   
0.1x  60 400  x  700
Using Graphing.xlsm.