6.2.1 Linear approximation at x = a

The linear approximation to f at x = a is the tangent line to f at x = a

This is a straight line f₁(x), which passes through x = a and has the same slope as f at x = a:

f₁(x) = f(a) + f '(a)(x - a)

These are the first two terms of the previous formula.

6.2.2 Quadratic approximation at x =a

The quadratic approximation to f at x = a is a quadratic, f₂ (x), which has the same value, derivative and second derivative as f at x  =a:

6.2.3 Cubic approximation at x = a

The cubic approximation to f at x  =a is a cubic, f₃ (x), which has the same value,

derivative, second derivative and third derivative as f at x = a: