The equation of the tangent line to the graph of a function at the point with abscissa x0.
Symbols
f′(x0)
derivative (slope)
x0
point of tangency
f(x0)
value of the function at x0
Where it comes from
The tangent line is a line whose slope equals the derivative at the point, passing through the point of tangency — the best linear approximation of the function.
When to use it
Finding the tangent line to the graph of a function at a given point.
Example
Find the tangent line to f(x)=x2 at x0=1 (f′(x)=2x).