In this section we learn how to find the equation of the tangent and the normal to a curve at a point along its length.
For each we learn a twp-step method as well as view a tutorial and work our way through exercises to consolidate our knowlede.
The following graph illustrates the tangent and the normal to the curve \(y=x^2-1\) at the point \(\begin{pmatrix}2,3\end{pmatrix}\):Given a function \(f(x)\), described by a curve \(y=f(x)\), we find the equation of the tangent to the curve at a point \(\begin{pmatrix}a,b\end{pmatrix}\) along its length, in two steps:
Find the equation of the tangent to the curve \[y = \frac{x^2}{2}+x + \frac{3}{2}\] at the point along its length with coordinates \(\begin{pmatrix}1,3\end{pmatrix}\).