Tangent Line Approximations

Definition

Tangent line approximations involve estimating the value of a function at a specific point by using the equation of its tangent line at that point. It provides a close approximation when working with small intervals around that point.

Related terms

Differentiability:

A function is differentiable if it has a derivative at every point in its domain. This property allows us to use tangent line approximations and other calculus techniques.

Local Linearization: Local linearization refers specifically to approximating functions using tangent lines near a particular point. It focuses on capturing behavior within a small neighborhood around that point.

Secant Line Approximations: Secant line approximations are similar to tangent line approximations but involve using secant lines instead. They provide estimates for average rates of change over larger intervals rather than instantaneous rates of change like tangents do.