Tangents and Normals
Derivatives are used to find a tangent and/or normal to a function at a specified point. You can use the derivative of a function to find the gradient of function at a point.
Tangents are lines that touch a function at a single point, however they do not intersect. Normals are the inverse of a tangent. A normal intersects the function perpendicular to the tangent, creating a 90-degree angle at the specified point.
To find the tangent of a function, you can plug an x-value into the derivative to find its gradient. The gradient of the function and the point can then be plugged into the point-slope formula, .
To find the normal, you can use the same process, but instead find the negative reciprocal of the slope of the tangent, this will be the slope of your normal.