1. Find the point
Evaluate the function at x₀. That gives the point (x₀, f(x₀)) that the tangent line must pass through.
Calculus · Interactive calculator
Tangent Line Calculator with a live graph
Enter a function and the x-value of the point. The tool estimates the derivative, writes the tangent equation, and lets you move a second point closer to see a secant become the tangent.
The calculation
A tangent line needs a point and a slope.
2. Find the slope
The derivative f′(x₀) is the limiting value of nearby secant slopes. This tool estimates it numerically from values on both sides.
3. Write the line
Use point-slope form y−f(x₀)=f′(x₀)(x−x₀), then rearrange if you want y=mx+b.