Taylor expansion

A Taylor expansion is a way to approximate a complex function using a sum of simpler terms, specifically polynomials. Imagine a curved line; near a specific point, it can be closely approximated by a polynomial that matches the function's value, slope, and curvature at that point. This series of terms, called the Taylor series, leverages derivatives (rates of change) to give increasingly accurate approximations near the chosen point. Essentially, it transforms complicated functions into easier-to-handle polynomials that behave very similarly close to the expansion point.