




The linear approximation to f at x = a is the tangent line to f at x = a
This is a straight line f_{1}(x), which passes through x = a and has the same slope as f at x = a:
f_{1}(x) = f(a) + f '(a)(x  a)
These are the first two terms of the previous formula.
The quadratic approximation to f at x = a is a quadratic, f_{2 }(x), which has the same value, derivative and second derivative as f at x_{ }=a:
The cubic approximation to f at x_{ }=a is a cubic, f_{3 }(x), which has the same value,
derivative, second derivative and third derivative as f at x = a: