Write a function my_der_calc(f,a,b,N,option), with the output as [df,X],where f(x) is a function that equals x(1-x), a and b are a scalars that represent the 1st and last point of your grid respectively, and Nis an integer that represents the number of grid points, and optionis the string that can take on the text forward, backward or central differencing. Thus, you are writing a function that can perform forward, backward or central differencing, the choice is determined by the input option Let xbe an array starting at a, ending at b, containing Nevenly spaced elements, and let y be the array f(x) The output argument, df, should be the numerical derivatives computed for xaccording to the method defined by the input argument, option The output argument Xshould be an array that is the same size as df containing the points in xfor which df is valid Remember, the forward difference method “loses” the last point, the backward difference method loses the first point, and the central difference method loses the first and last points. So you have to use forward or backward differences depending on whether it is the 1st or last point. Plot df .vs X, notice the functional form of your plot. Compare with the actual form with the derivative of the given function, if the calculated derivative is not within 1×〖10〗^(-3) of the given function derivative add more points until the calculated derivative is less than or equal to 1×〖10〗^(-3) of the given function’s derivative Write a derivative function that doesn’t use numpy arrays

C++ Programming: From Problem Analysis to Program Design

8th Edition

ISBN:9781337102087

Author:D. S. Malik

Publisher:D. S. Malik

Chapter6: User-defined Functions

Section: Chapter Questions

Problem 17PE

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Write a function my_der_calc(f,a,b,N,option), with the output as [df,X],where f(x)
is a function that equals x(1-x), a and b are a scalars that represent the 1st and last point of your grid respectively, and Nis an integer that represents the number of grid points, and optionis the string that can take on the text forward, backward or central differencing. Thus, you are writing a function that can perform forward, backward or central differencing, the choice is determined by the input option
Let xbe an array starting at a, ending at b, containing Nevenly spaced elements, and let y be the array f(x)
The output argument, df, should be the numerical derivatives computed for xaccording to the method defined by the input argument, option
The output argument Xshould be an array that is the same size as df containing the
points in xfor which df is valid
Remember, the forward difference method “loses” the last point, the backward difference method loses the first point, and the central difference method loses the first and last points. So you have to use forward or backward differences depending on whether it is the 1st or last point.
Plot df .vs X, notice the functional form of your plot.
Compare with the actual form with the derivative of the given function, if the calculated derivative is not within 1×〖10〗^(-3) of the given function derivative add more points until the calculated derivative is less than or equal to 1×〖10〗^(-3) of the given function’s derivative
Write a derivative function that doesn’t use numpy arrays

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