2. Numerical Differentiation (a) Create a python file that numerically estimates the derivative of a vector of function values. The inputs for the file will be a vector (list) x of equally-spaced values together with a vector (list) of y values for the associated x values. The output of the python file should be a vector (list) of the numerical approximation of the derivative of y with accuracy of order O(ha). (b) The following data represents the velocity v of a Saturn 5 rocket over equally spaced time values t. Use your python file from (a) to estimate the acceleration of the rocket for all time values. Include a plot that shows the velocity and approximated acceleration versus time. Time (secs) 0 2 4 7 9 10 Velocity (15) 0 3 4 7 10 12 15 16 20 23 25 1 3 5 6 8