Assess learners' ability to apply the Newton–Raphson method to solve nonlinear scalar equations: perform iterative updates from a given initial guess, compute and use derivatives, select stopping criteria, estimate and report errors and the observed convergence order, diagnose convergence issues (divergence, slow convergence, multiple roots, near-zero derivatives), and propose practical remedies (damping, modified Newton, reinitialization); include one worked example and interpretation of results.