Let the function f(x) = tx3 + ux2 + vx +w, where t = 1, u = -3, v = -130, and w = 150. The equation is utilized in analytic chemistry, but for the purposes is just the nice polynomial.
i) Find analytical (exact) derivative of f?
ii) Compute derivative by using forward differences.
iii) Find derivative using centered differences. Utilize Excel to make calculations.