$$f^\prime(x)=\lim_{h \rightarrow 0}{{f(x+h)-f(x)} \over h}$$
**Tangent line** of function $f$ at point $M(a, f(a))$ is the line through $M$ with gradient $f^\prime(a)$.
+
+## Tangents and gradients
+
+
+### Tangent of a point
+
+For a point $P(q,r)$ on function $f$, the gradient of the tangent is the derivative $dy \over dx$ of $f(q)$. Therefore the tangent line is defined by $y=mx+c$ where $m={dy \over dx}$. Substitute $x=q, \hspace{0.5em} y=q$ to solve for $c$.
+
+### Normal
+
+Normal $\perp$ tangent.
+
+$$m_{\operatorname{tan}} \cdot m_{\operatorname{norm}} = -1$$
+
+Normal line for point $P(q,r)$ on function $f$ is $y=mx+c$ where $m={-1 \over m_{\tan}}$. To find $c$, substitute $(x, y)=(q,r)$ and solve.
+
+### Solving on CAS
+
+**In main**: type function. Interactive -> Calculation -> Line -> (Normal | Tan line)
+**In graph**: define function. Analysis -> Sketch -> (Normal | Tan line). Type $x$ value to solve for a point. Return to show equation for line.