Question

For this problem, you must create a table of values for x in [−1, 1] with a separation of h = 0.02 for the function f(x) = x5 − 0.36x3 + .2563. Then create the table for the approximate f′(x), as in the example problem. Make sure to format the cells as Number so values appear correctly. For the cells in columns B and C, use decimal numbers with 6 places. Once the table is created, make the scatterplot that shows the plots for both functions.

Problem #2 (8 points total)
Repeat the previous process for f (x) = ex with h = 0.01 for x in [−1, 1].

Note: in Excel, the formula “exp(x)” is the formula for the natural exponential function, with the cell you are referencing in place of “x”.

Answer 1

1. We have

So

x	f(x)	f'(x)
-1.00000	-0.38370	3.92000
-0.98000	-0.30879	3.57461
-0.96000	-0.24057	3.25140
-0.94000	-0.17859	2.94946
-0.92000	-0.12245	2.66785
-0.90000	-0.07175	2.40570
-0.88000	-0.02610	2.16212
-0.86000	0.01485	1.93627
-0.84000	0.05146	1.72731
-0.82000	0.08405	1.53442
-0.80000	0.11294	1.35680
-0.78000	0.13842	1.19368
-0.76000	0.16078	1.04430
-0.74000	0.18028	0.90792
-0.72000	0.19718	0.78382
-0.70000	0.21171	0.67130
-0.68000	0.22410	0.56968
-0.66000	0.23457	0.47829
-0.64000	0.24330	0.39649
-0.62000	0.25048	0.32366
-0.60000	0.25630	0.25920
-0.58000	0.26090	0.20251
-0.56000	0.26445	0.15304
-0.54000	0.26707	0.11022
-0.52000	0.26890	0.07355
-0.50000	0.27005	0.04250
-0.48000	0.27063	0.01659
-0.46000	0.27074	-0.00466
-0.44000	0.27047	-0.02168
-0.42000	0.26990	-0.03493
-0.40000	0.26910	-0.04480
-0.38000	0.26813	-0.05170
-0.36000	0.26705	-0.05599
-0.34000	0.26591	-0.05803
-0.32000	0.26474	-0.05816
-0.30000	0.26359	-0.05670
-0.28000	0.26248	-0.05394
-0.26000	0.26144	-0.05016
-0.24000	0.26048	-0.04562
-0.22000	0.25962	-0.04056
-0.20000	0.25886	-0.03520
-0.18000	0.25821	-0.02974
-0.16000	0.25767	-0.02437
-0.14000	0.25723	-0.01925
-0.12000	0.25690	-0.01452
-0.10000	0.25665	-0.01030
-0.08000	0.25648	-0.00671
-0.06000	0.25638	-0.00382
-0.04000	0.25632	-0.00172
-0.02000	0.25630	-0.00043
0.00000	0.25630	0.00000
0.02000	0.25630	-0.00043
0.04000	0.25628	-0.00172
0.06000	0.25622	-0.00382
0.08000	0.25612	-0.00671
0.10000	0.25595	-0.01030
0.12000	0.25570	-0.01452
0.14000	0.25537	-0.01925
0.16000	0.25493	-0.02437
0.18000	0.25439	-0.02974
0.20000	0.25374	-0.03520
0.22000	0.25298	-0.04056
0.24000	0.25212	-0.04562
0.26000	0.25116	-0.05016
0.28000	0.25012	-0.05394
0.30000	0.24901	-0.05670
0.32000	0.24786	-0.05816
0.34000	0.24669	-0.05803
0.36000	0.24555	-0.05599
0.38000	0.24447	-0.05170
0.40000	0.24350	-0.04480
0.42000	0.24270	-0.03493
0.44000	0.24213	-0.02168
0.46000	0.24186	-0.00466
0.48000	0.24197	0.01659
0.50000	0.24255	0.04250
0.52000	0.24370	0.07355
0.54000	0.24553	0.11022
0.56000	0.24815	0.15304
0.58000	0.25170	0.20251
0.60000	0.25630	0.25920
0.62000	0.26212	0.32366
0.64000	0.26930	0.39649
0.66000	0.27803	0.47829
0.68000	0.28850	0.56968
0.70000	0.30089	0.67130
0.72000	0.31542	0.78382
0.74000	0.33232	0.90792
0.76000	0.35182	1.04430
0.78000	0.37418	1.19368
0.80000	0.39966	1.35680
0.82000	0.42855	1.53442
0.84000	0.46114	1.72731
0.86000	0.49775	1.93627
0.88000	0.53870	2.16212
0.90000	0.58435	2.40570
0.92000	0.63505	2.66785
0.94000	0.69119	2.94946
0.96000	0.75317	3.25140
0.98000	0.82139	3.57461
1.00000	0.89630	3.92000

and the corresponding scatterplot of f(x) and f'(x) using the values in the table is

here blue is f(x) and orange is f'(x)