Differentiating CBD

Differentiating CBD - DIFFERENTIATING A FUNCTION 1. Set...

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Unformatted text preview: DIFFERENTIATING A FUNCTION 1. Set Excel for Automatic Calculation. 2. Enter a formula, in terms of the letter x, for = f(x) in Cell C24. Constants s, t, u, v, or w may be used; if values are entered in Cells O24:O27. (The value of f(0) will appear in Cell C24.) 3. Click on the Differentiate button located to the right of the plot regions. This runs the macro, Differentiate. 4. Cell F24 will display the value of f(x) for any number x that is entered in Cell E24 and Cell G24 will display the value of f '(x) for that number. 5. Enter values for a and b in Cells I 24 and J24, to see the graphs of f(x) and f '(x) over the interval [a, b]. Constants s, t, u, v, or w may be used; if values are entered in Cells O23:O27. If these constant names are used, they must be entered in Cells I24:J24 preceded with "=" signs. For example, =s. 6. Scroll down to see the graphs of f(x) and f '(x) plotted on the same set of axes. 7. If the computed values or the graphs are inaccurate, try a different value for the increment, h, that is entered in Cell L24. 8. If f '(x) is constant, the displayed plot will be distorted. To correct this, format the yaxis to have fixed minimum and maximum values. Definition Formula for f(x) = x Computation f(x) f '(x) = 0.000 Plot Interval a b FUNCTION 12 10 8 f(x) 6 4 2 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 x 1 0.9 0.8 0.7 0.6 0.5 f'(x) 0.4 0.3 0.2 0.1 0 DERIVATIVE 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 x 2 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 x 0.2 0.1 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 x FUNCTION & DERIVATIVE 1 0.9 0.8 0.7 0.6 f(x) 0.5 f'(x) 0.4 0.3 0.2 0.1 0 0 0.1 0.2 0.3 0.4 0.5 x 0.6 0.7 0.8 0.9 1 Column U Column V stants s, t, u, v, will appear in ons. This runs ed in Cell E24 (x) and f '(x) over in Cells 24:J24 preceded et of axes. alue for the his, format the y- Calculus for Business Decisions Release 2.1, 2010 Published and Distributed by The Mathematical Association of America © 2010 by The Arizona Board of Regents for The University of Arizona. All rights reserved. Increment h 0 VATIVE Constants s t u v w 0.4 0.5 0.6 0.7 0.8 0.9 1 x 0.4 0.5 0.6 0.7 0.8 0.9 1 x Column U Column V r Business Decisions ase 2.1, 2010 and Distributed by al Association of America izona Board of Regents for of Arizona. All rights reserved. f(var) = P4 step size Index 0 value 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 f(values) f '(value) = = 0 = f(value) 0 = 0 = 0 = 0 = 0 = 0 = 0 = 0 = 0 = 0 = 0 = 0 = 0 = 0 = 0 = 0 = 0 = 0 = 0 = 0 = 0 = 0 = 0 = 0 = 0 = 0 = 0 = 0 = 0 = 0 = 0 = 0 = 0 = 0 = 0 = f '(value) val-h 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 f(val-h) 0 = 0 = 0 = 0 = 0 = 0 = 0 = 0 = 0 = 0 = 0 = 0 = 0 = 0 = 0 = 0 = 0 = 0 = 0 = 0 = 0 = 0 = 0 = 0 = 0 = 0 = 0 = 0 = 0 = 0 = 0 = 0 = 0 = 0 = 0 = val+h 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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This note was uploaded on 10/27/2010 for the course ECE 220 taught by Professor Strickland during the Spring '08 term at University of Arizona- Tucson.

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