finite difference formula in matlab

1 Using MATLAB, write a program (.m file) to compute an approximate value of the derivative of a function using the following finite difference formula.

2 Test your program using the function tan 𝑥 for 𝑥 = 1. Determine the error by comparing with the square of the built-in function sec (𝑥).

3 Graph the magnitude of the error as a function of ℎ, for ℎ = 10^(−k), 𝑘 = 0,…, 16. You should use logarithmic scale for ℎ and also for the magnitude of the error.

4 Is there a minimum value for the magnitude of the error?

5 How does the corresponding value for ℎ compare with the rule of thumb ℎ ≈ √𝜀𝑚𝑎𝑐ℎ?

6 Repeat items 1 through 5 using the central difference approximation.

[Sulaymon Eshkabilov]

It looks like a student assignment. Could you pl., show here your attempted actions (written codes)?