Linearization and Tangent Line Approximations

Definition

Linearization involves approximating a function near a specific point using its tangent line. Tangent line approximations provide close estimates for function values based on linear behavior around a given point.

Related terms

Derivative:

The derivative of a function represents its rate of change at any given point and is crucial for finding tangent lines and linearizations.

Local Linearity: Local linearity refers to the property of functions where they can be approximated by linear behavior within small intervals around specific points.

Taylor Series:

A Taylor series is an expansion of a function into an infinite sum of terms, allowing us to approximate functions using polynomials.