4. Let f (x) = Inx - x + x2 +3x. Apply a) two, and b) three-point formulas of Table 4.3 (given below) to estimate derivatives of f (x) at Xo = 1. Use two step size h = 10-2 and h = 10-3. find actual error by comparison with the analytical derivatives. TABLE 4.3 Some Popular Derivative Approximations First derivative approximations Three-point f' (x) _ f ( x + h) - f(x - h) + o(h?) 2h Four-point f' (x) = =f( x + 2h) + 6f(x + h) - 3f(x) - 2f(x - h) + o(h3) 6h Five-point f' (x) = =2f(x + 2h) + 16f(x + h) - 16f(x - h) + 2f(x -2h) + 0(h") 24h Second derivative approximations Three-point f" (x) = f(x + h) -2f(x)+f(x -h) + O(h? ) h2 Four-point Coincides with three-point formula Five-point f" (x) _ _f(x + 2h) + 16f(x + h) - 30f(x) + 16f(x - h) - f(x - 2h) 12h2 + O(h')