A tangent line is a line that passes through a given point and has the same slope as the function at that point. The point of tangency describes the location where the tangent line and the function intersect.

Formula

The line tangent to the function is given by the following equation

Where is the point where the line is called the point of tangency

Example

Given the function find the tangent line at .

The function is shown in red, the point on the graph at is shown as a red dot, and the tangent line to the function at is shown in blue.