Using Five point Forward difference, Backward difference, Central difference formula numerical differentiation to find solution

x	1	1.05	1.10	1.15	1.20	1.25	1.30
f(x)	1	1.02470	1.04881	1.07238	1.09545	1.11803	1.14018

`f^'(1.15) and f^('')(1.15)`

Solution:
The value of table for `x` and `y`

x	1	1.05	1.1	1.15	1.2	1.25	1.3
y	1	1.0247	1.0488	1.0724	1.0954	1.118	1.1402

Five-point CDF (Central difference formula)
`f^'(x)=1/(12h)[f(x-2h)-8f(x-h)+8f(x+h)-f(x+2h)]`

`f^'(1.15)=1/(12*0.05)[f(1.15-2*0.05)-8f(1.15-0.05)+8f(1.15+0.05)-f(1.15+2*0.05)]`

`f^'(1.15)=1/0.6[f(1.05)-8f(1.1)+8f(1.2)-f(1.25)]`

`f^'(1.15)=1/0.6[1.0247-8(1.0488)+8(1.0954)-1.118]`

`f^'(1.15)=0.4663`

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Five-point CDF (Central difference formula) for second derivatives
`f^('')(x)=1/(12h^2)[-f(x-2h)+16f(x-h)-30f(x)+16f(x+h)-f(x+2h)]`

`f^('')(1.15)=1/(12*(0.05)^2)[-f(1.15-2*0.05)+16f(1.15-0.05)-30f(1.15)+16f(1.15+0.05)-f(1.15+2*0.05)]`

`f^('')(1.15)=1/0.03[-f(1.05)+16f(1.1)-30f(1.15)+16f(1.2)-f(1.25)]`

`f^('')(1.15)=1/0.03[-1.0247+16(1.0488)-30(1.0724)+16(1.0954)-1.118]`

`f^('')(1.15)=-0.199`

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