Editing Newton's method in optimization (section)

==Geometric interpretation==

The geometric interpretation of Newton's method is that at each iteration, it amounts to the fitting of a [[parabola]] to the [[Graph of a function|graph]] of <math>f(x)</math> at the trial value <math>x_k</math>, having the same slope and curvature as the graph at that point, and then proceeding to the maximum or minimum of that parabola (in higher dimensions, this may also be a [[saddle point]]), see below. Note that if <math>f</math> happens to {{em|be}} a quadratic function, then the exact extremum is found in one step.