Kissing the curve – the gruesome details
So, you want to more? Here are all the gruesome details for calculating the tangent, normal, curvature and osculating circle of a curve!
Think of your favourite smooth curve in a plane that can be described by a function, . Then at any point , the slope of the tangent line is just the value of the derivative of the function at that point, . With this information, and the fact that the tangent must pass through the point , we can work out that the equation for the tangent is
Go back to the article or play with the worksheet below.
You can use this geogebra worksheet to see the tangent, normal and osculating circle of any smooth curve you choose - just change the equation f(x) in the left-hand panel.