What is the linear approximation formula?

The linear approximation formula is f(x) is approximately equal to f(x0) + f'(x0) x (x - x0), where f'(x) denotes the derivative of f(x). The linear approximation formula is based on the affine function and is used in math to approximate the difference between two vector functions.

The linear approximation formula results in an overestimation if the interval between x and x0 is concave downwards, whereas the formula results in an underestimation if that area is concave upwards. The formula is based upon a concept in calculus known as Taylor's theorem, which is used to find the function for a given point for a polynomial function.