http://www.ck12.org Chapter 2. Derivatives
Figure 8a
Figure 8b
So for values ofxclose tox 0 , the values ofyof this tangent line will closely approximatef(x). This gives the
approximation
f(x) =f(x 0 )+f′(x 0 )(x−x 0 ).The Tangent Line Approximation (Linearization)
Iffis a differentiable function atx=x 0 , then the approximation function
L(x) =f(x)≈f(x 0 )+f′(x 0 )(x−x 0 )