Part 2/8:
In the realm of calculus, we often need to find ways to approximate complex functions. A simple method we have encountered is linear approximation, which involves drawing the tangent line to a curve at a specific point. The equation of this tangent line allows us to estimate values of the function near that point.
However, linear approximation might not always yield satisfactory results, especially for functions that exhibit curvature or higher-order behavior. Hence, we turn to quadratic approximations and subsequently, higher degree polynomials, which help to refine our predictions further.