3. Award: 10.00 points In section 4.4, an optimal step size formula, hopt 3 3 = M for the central difference for the first derivative 1 is derived. A) Derive similar formula to the forward difference. B) Use forward difference approximations of O(h) to estimate the first derivative of the function f(x) = -0.1x4 0.15x3 0.5x2 0.25x + 1.2 at x = 0.5 using a step size h = 1, 10-1,10-2,...,10-10 then calculate the true error at these approximations. C)plot step size .vs. true error and investigate that the formula obtained in part A) is consistent. [Hint: see EXAMPLE 4.5 page 127] 3. Award: 10.00 points In section 4.4, an optimal step size formula, hopt 3 3 = M for the central difference for the first derivative 1 is derived. A) Derive similar formula to the forward difference. B) Use forward difference approximations of O(h) to estimate the first derivative of the function f(x) = -0.1x4 0.15x3 0.5x2 0.25x + 1.2 at x = 0.5 using a step size h = 1, 10-1,10-2,...,10-10 then calculate the true error at these approximations. C)plot step size .vs. true error and investigate that the formula obtained in part A) is consistent. [Hint: see EXAMPLE 4.5 page 127]