$$f^\prime(x)=\lim_{h \rightarrow 0}{{f(x+h)-f(x)} \over h}$$
+Not differentiable at:
+
+- discontinuous points
+- sharp point/cusp
+- vertical tangents ($\infty$ gradient)
+
## Tangents & gradients
**Tangent line** - defined by $y=mx+c$ where $m={dy \over dx}$
**Normal line** - $\perp$ tangent ($m_{\operatorname{tan}} \cdot m_{\operatorname{norm}} = -1$)
**Secant** $={{f(x+h)-f(x)} \over h}$
+$$\tan \Theta = m = f^\prime x$$
+
+where $\Theta$ is the angle that tangent line makes with +ve direction of $x$-axis
+
+## Strictly increasing
+
+- Function $f$ is **strictly increasing** where $f(x_2) > f(x_1)$ and $x_2 > x_1$
+- Function $f$ is **strictly decreasing** where $f(x_2) < f(x_1)$ and $x_2 > x_1$
+- If $f^\prime (x) > 0$ for all $x$ in interval, then $f$ is **strictly increasing**
+- If $f^\prime(x) < 0$ for all $x$ in interval, then $f$ is **strictly decreasing**
+- Endpoints are included, even where gradient $=0$
+
### Solving on CAS
**In main**: type function. Interactive -> Calculation -> Line -> (Normal | Tan line)