I need help with the questions from:

• Now determine the first derivative f ( x ) analytically. Calculate the total absolute error n = 0 10 f ( x n ) g ( x n ) between the analytical derivative f ( x ) and the central difference approximation g ( x ) = f ( x + h ) f ( x h ) 2 h. Round the answer correct to the fourth decimal place ______________________
• If the interval [ , 2 ] is discretized using the new step h = 100, what is the new value of the total error n = 0 100 f ( x n ) g ( x n ) ? Round the answer correct to the fourth decimal place .______________________
• The central difference approximation for the second derivative is f ( x ) f ( x + h ) + f ( x h ) 2 f ( x ) h 2 + O ( h n ). Give the value of ________________

Please provide the MatLab code so that I am able to cross check.

The function f(x) = x cos(3.c) is discretized on the interval 2 7,21] using equidistant grid with step h = 7/10 so that the grid points are located aten = 7+nh, (n = 0, 1, ..., 10). Use central difference approximation to determine the value of the first derivative of f(2) at 27 = . Round the answer correct to the fourth decimal place 3.6910 (Hint: By default Matlab rounds the answer to the fourth decimal place.) Use central difference approximation to determine the value of the second derivative of f(x) at 2g = Round the answer correct to the fourth decimal place -25.141 Use forward difference approximation to determine the value of the first derivative of f(x) at x5 = 37. Round the answer correct to the fourth decimal place -12.944 Use backward difference approximation to determine the value of the first derivative of f(2) at 28 = Round the answer correct to the fourth decimal place 10.606 Now determine the first derivative f'(2) analytically. Calculate the total absolute error 10. f'(an) - glan) between the analytical derivative f' (x) and the central difference approximation g(x) = f(a+h)f(2-). Round the answer correct to the fourth 2h decimal place If the interval 1,27] is discretized using the new step h = 100, what is the new value of the total error 100 f'(an) - g(xn)? Round the answer correct to the fourth decimal place f(+h)-f(-h)-2ft The central difference approximation for the second derivative is f"(x) ! ohn). Give the value of n = The function f(x) = x cos(3.c) is discretized on the interval 2 7,21] using equidistant grid with step h = 7/10 so that the grid points are located aten = 7+nh, (n = 0, 1, ..., 10). Use central difference approximation to determine the value of the first derivative of f(2) at 27 = . Round the answer correct to the fourth decimal place 3.6910 (Hint: By default Matlab rounds the answer to the fourth decimal place.) Use central difference approximation to determine the value of the second derivative of f(x) at 2g = Round the answer correct to the fourth decimal place -25.141 Use forward difference approximation to determine the value of the first derivative of f(x) at x5 = 37. Round the answer correct to the fourth decimal place -12.944 Use backward difference approximation to determine the value of the first derivative of f(2) at 28 = Round the answer correct to the fourth decimal place 10.606 Now determine the first derivative f'(2) analytically. Calculate the total absolute error 10. f'(an) - glan) between the analytical derivative f' (x) and the central difference approximation g(x) = f(a+h)f(2-). Round the answer correct to the fourth 2h decimal place If the interval 1,27] is discretized using the new step h = 100, what is the new value of the total error 100 f'(an) - g(xn)? Round the answer correct to the fourth decimal place f(+h)-f(-h)-2ft The central difference approximation for the second derivative is f"(x) ! ohn). Give the value of n =