Consider the data given below: -50 -25 25 50 75 100 125 F(x) -39 -20 round(44/10) 32 5+4/5 67 79 83 At the x value which is closest to 44, calculate the derivative of f(x) using a suitable second...

At the x value which is closest to 44, calculate the derivative of f(x) using a suitable second order accurate finite difference method with a) h = 25, b) a different step size. (You should use the same finite difference method in (a) and (b)).

Using the values you calculated at parts (a) and (b) apply Richardson
extrapolation to improve your calculation.

Extracted text: Consider the data given below: -50 -25 25 50 75 100 125 F(x) -39 -20 round(44/10) 32 5+4/5 67 79 83 At the x value which is closest to 44, calculate the derivative of f(x) using a suitable second order accurate finite difference method with a) h = 25, b) a different step size. (You should use the same finite difference method in (a) and (b)). Using the values you calculated at parts (a) and (b) apply Richardson extrapolation to improve your calculation.