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(Solved): Given the following data points x_(i)=[-1,-0.8,-0.6,-0.4,-0.2,0,0.2,0.4,0.6,0.8,1] f_(i)=[14.7781,9. ...



Given the following data points

x_(i)=[-1,-0.8,-0.6,-0.4,-0.2,0,0.2,0.4,0.6,0.8,1] f_(i)=[14.7781,9.9061,6.6402,4.4511,2.9836,2.0,1.3406,0.8987,0.6024,0.4038,0.2707]

Find the derivative

f^(')(0.4)

using the following methods: a)

1^(st )

order forward difference. b)

2^(nd )

order forward difference. c)

1^(st )

order backward difference. d)

2^(nd )

order backward difference. e)

2^(nd )

order central difference. f)

4^(th )

order central difference. Find

\int_(-1)^1 f(x)dx

using the following methods: a) Trapezoidal Rule b) Simpson's

(1)/(3)

Rule. c) Simpson's

(3)/(8)

Rule (from

x=-1

to

x=0.8

) and Trapezoidal Rule (

x=

0.8 to

x=1

) "Note: Show your detailed work."

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