Mathematics & Statistics / Calculus
Tangent Line Equation Generator
Tangent Line at Point
Formula
y - f(a) = f'(a)(x - a)
Where f'(a) is the derivative at point a
Generate tangent line equations at specific points to translate derivative output into local linear approximations.
Formula
Tangent line at x = a: y - f(a) = f'(a)(x - a)
Worked Example
functionx^2
pointX3
Result: y = 6x - 9Derivative at x=3 is 6, and the tangent passing through (3,9) yields the linear equation y = 6x - 9.
Frequently Asked Questions
What is the difference between tangent and secant lines?
A secant uses two points on a curve; a tangent is the limiting secant at one point with instantaneous slope.
Why is tangent line useful?
It provides local linear approximation, often used for estimation and error analysis.