# Linear Approximation Calculator

> Calculate the tangent line approximation L(x) = f(a) + f'(a)(x - a) for any mathematical function f(x). Compares the linear estimate against the true function value and calculates absolute error.

**URL:** https://www.calculatoranswers.com/linear-approximation-calculator
**Category:** Education

## Quick Answer

Calculate the linear tangent approximation L(x) = f(a) + f'(a)(x - a) of a function f(x) near a center point a.

## Definition

A linear approximation calculator computes the tangent line approximation of a function f(x) at a center point a. Using symbolic derivatives (with numerical differentiation fallbacks), it formats the point-slope and slope-intercept equations of the tangent line L(x), evaluates the approximation at target x, and computes the error |f(x) - L(x)|.

## How to Use

1. **Enter function parameters** — Input the function expression f(x), the center point (a), and the evaluation point (x).
2. **Review derivatives** — See f(a) and the derivative f'(a) evaluated at the center point.
3. **Read results** — View the tangent line equations, the approximated value L(x), and the absolute approximation error.

## Disclaimer

This calculator provides estimates for educational and planning purposes. Always consult a qualified professional for specific advice on financial, medical, legal, or other regulated decisions.

---

*This page is part of Calculator Answers — simple calculators, clear answers, no signup required. View all calculators at https://www.calculatoranswers.com/calculators*