(a) Use the Taylor series expansion to derive a three-point finite difference formula that evaluates the first derivative dy/dx at point x=x; with given points (x₁,Yi), (Xi+1, Yi+1), (Xi+2, Yi+2), which are not equally spaced. Use three terms of the series plus the remainder. (b) Derive for the case when the spacing between the points is equal, a simpler finite difference formula. (c) Use the data in the table to derive in a MatLab scipt the derivative of the point x=x₁. No MatLab build-in function is allowed to be used. Submit for (a) and (b) your hand calculations and for (c) your MatLab files. Xi 5.49 Xi+1 5.58 Xi+2 5.63 Yi 8.08 Yi+1 8.12 Yi+2 8.15

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