Question

5. Using 3-point formulas, complete the following table with estimates for f' and f". f(x)| f'(x) | S"(x) 2.0 6.00 2.2 6.02 2.4 6.06 2.6 6.12 2.8 6.16

Answer 1

Svin - Three both to point before better formula allow us to and after the point evaluate the derinative. use to information be evaluated from f'oi) = f(a+h) - f(x-hd. 2h t'= frach) - 2.4(^3 + f(x+h) 62 : : 2.1 2.0 | 22 | 2.4 | 2.6 2.8 fons I 6.00 6.02 6.00 | 612 | 6:16 There, h= 0.02 {we can't start from n=200 ... is when a = 2-2 ? as f(108) is not given} fény = f(a+h) - flach ) zh faou) - $(2.0) 2x 0.2 6.06 - 6 - 2x 0-2 0015 f'm = f(2.0) - 24(2-2) + f(2.4) (0.2) 6 - 2x 6002 + 6:06' = 0.5 CO2)2 = CS Scanned with CamScanner

when x= 204 fin) = f(2-6) -412-2) 2x 0.2 = 6•12 - 6.02 : 2x 0.2 - 025 L ifan = f(2:2) -2of(2.0) + f(2-6) (0. 2² 6.02 - 2x 6.06 + 6012 2 (0-2) = 0.5 in inhen x=2-6 fin) = f(768) – 'f(204) AZ2X2 - 6-16 - 6.06 2x0-2 30:25 fes = f(201) - 2 f(206) + f(208) . (0272 606 - 2x 6-12 + 6016 [002)² : Scanned with CamScanner. - 0.5

ANSWER f'(202) = 0.15. f" (202) = 0.5. f" (204) = 005 f'(204) = 0025 f'(2-6) = 0.25 f'(2-6) = -005 CS Scanned with CamScanner