\fDefinition If y = f(x) is differentiable at a = a, then the approximationg function is given by the formula f ( x ) = f' ( a) ( x- a ) + f (a ] y- fla) = fla) (x-a) this is the tangent line tof at x= a and is called the linear approximation or tangent line approximation of f at a. The linearization of f at a is L ( x) = f' la) ( x-a)+ fca) The linearization is literally the tangent line for at a