
6-16 Calculus – Differentiation and Integration
However, we can obtain an approximate value of the function y = f(x) at points close to the point
x = a using the tangent line to the curve at a. The main idea of linearization (linear approximation)
lies in the closeness of the tangent line to the graph of the function around a point. Let us find the
equation of the tangent line at the point (a, f(a)) to have a clear understanding of the idea behind
the concept.
Since the slope of the tangent line at the point (a, f(a)) is f ′(a), the equation of the tangent line using
point-slope formula is given as
y y
dy
dx
x x
y f a f ' a x a
x y
− =