Tangent Line Approximation and Differentials

In general, for a differentiable function f, the equation of the tangent line to f at x = a can be used to approximate f(x) for x near a. Therefore, we can write f(x) ≈ f(a) + f ′ (a)(x − a) for x near a. We call the linear function L(x) = f(a) + f ′ (a)(x − a) the linear approximation, or tangent line approximation...