Given a function f : R⟶R that is continuously differentiable on  x∈{x−k,...,xn−2,xn−1,xn,xn+1,xn+2,...,xk}⊂R, use the Taylor series to derive the second-order accurate approximations for the following: forward difference formula for f′(xn), backward difference formula for f′(xn), and central difference formula for f′(xn).

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