Second Derivative - Quadratic Approximation

Quadratic Approximation

Just as the first derivative is related to linear approximations, the second derivative is related to the best quadratic approximation for a function ƒ. This is the quadratic function whose first and second derivatives are the same as those of ƒ at a given point. The formula for the best quadratic approximation to a function ƒ around the point x = a is

This quadratic approximation is the second-order Taylor polynomial for the function centered at x = a.