1) Implement a numerical differentiation using the secant method with fixed, but variable (user input) stepsize. Calculate at 0,pi/4,pi/2, 3/4pi and pi the differntial of sin(x) and compare
your results to the analytical expectation.
Remark: Apparently the secant method “name” is referring to root-finding, even though the algorithms are similar, what I was refering too is the definition of the first derivative as the tangent as
being the limit of secants. f'(x)=lim h->0 (f(x+h)-f(x))/h. Sorry for the potential confusion. Also be aware that this brute-force method is sensitive to rounding and precision since you have a
difference close to zero divided by a small number. So play around with “reasonable” values of h. For a detailed discussion look at the Numerical Recipes.