Description
Consider the function
f(x) = sin(4.8 π x).
Compute the derivative by hand to get the truth. Implement the following
numerical methods for approximating first derivatives: (i) one-sided forward
difference, (ii) one-sided backward difference, and (iii) central difference. Use
the numerical methods to estimate the derivative at some value of x.
Study the convergence of the finite difference approximations. Choose
several values of h and compute the error for each, then plot the relationship. Identify the asymptotic regime to estimate the convergence rate of each
method. Do the rates depend on x?
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