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.