[spec] DEs of the dependent variable

diff --git a/methods/calculus-ref.md b/methods/calculus-ref.md
index 215845dc033695058ee7b9f03272b801100faf46..e12b37e76611a8ec1714f7877ef26ab7f979510e 100644 (file)
--- a/methods/calculus-ref.md
+++ b/methods/calculus-ref.md
@@ -1,25 +1,29 @@
 ---
-geometry: margin=1cm
+geometry: a4paper, margin=2cm
 columns: 2
-graphics: yes
-tables: yes
 author: Andrew Lorimer
 header-includes:
+- \usepackage{fancyhdr}
+- \pagestyle{fancy}
+- \fancyhead[LO,LE]{Year 12 Methods}
+- \fancyhead[CO,CE]{Andrew Lorimer}
+- \usepackage{graphicx}
 - \usepackage{tabularx}
+- \usepackage[dvipsnames, table]{xcolor}
 ---
 
-
+\linespread{3}
 \pagenumbering{gobble}
 \renewcommand{\arraystretch}{1.4}
+\definecolor{cas}{HTML}{e6f0fe}
 
-
-# Methods - Calculus
+# Calculus
 
 ## Average rate of change
 
 $$m \operatorname{of} x \in [a,b] = {{f(b)-f(a)}\over {b - a}} = {dy \over dx}$$
 
-On CAS: Action $\rightarrow$ Calculation $\rightarrow$ Diff $\rightarrow$ ($f(x)$ | $y$) $=\dots$
+\colorbox{cas}{On CAS:} Action $\rightarrow$ Calculation $\rightarrow$ `diff`
 
 ## Instantaneous rate of change
 
@@ -51,18 +55,22 @@ Not differentiable at:
 **Normal line** - $\perp$ tangent ($m_{{tan}} \cdot m_{\operatorname{norm}} = -1$)  
 **Secant** $={{f(x+h)-f(x)} \over h}$
 
-## Strictly increasing
+## Strictly increasing/decreasing
 
-- **strictly increasing** where $f(x_2) > f(x_1)$ and $x_2 > x_1$
-- **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**
+For $x_2$ and $x_1$ where $x_2 > x_1$:
+
+- **strictly increasing** where $f(x_2) > f(x_1)$  
+or $f^\prime(x)>0$
+- **strictly decreasing** where $f(x_2) < f(x_1)$  
+or $f^\prime(x)<0$
 - Endpoints are included, even where gradient $=0$
 
+\columnbreak
+
 ### Solving on CAS
 
-**In main**: type function. Interactive $\rightarrow$ Calculation $\rightarrow$ Line $\rightarrow$ (Normal | Tan line)  
-**In graph**: define function. Analysis $\rightarrow$ Sketch $\rightarrow$ (Normal | Tan line). Type $x$ value to solve for a point. Return to show equation for line.
+\colorbox{cas}{\textbf{In main}}: type function. Interactive $\rightarrow$ Calculation $\rightarrow$ Line $\rightarrow$ (Normal | Tan line)  
+\colorbox{cas}{\textbf{In graph}}: define function. Analysis $\rightarrow$ Sketch $\rightarrow$ (Normal | Tan line). Type $x$ value to solve for a point. Return to show equation for line.
 
 ## Stationary points
 
@@ -87,11 +95,14 @@ Find derivative, solve for ${dy \over dx} = 0$
 
 ## Function derivatives
 
-\begin{tabularx}{\columnwidth}{rl}
+\definecolor{shade1}{HTML}{ffffff}
+\definecolor{shade2}{HTML}{F0F9E4}
+\rowcolors{1}{shade1}{shade2}
+\begin{tabularx}{\columnwidth}{rX}
   
   \hline \(f(x)\) & \(f^\prime(x)\) \\ \hline
 
-  \(kx^n\) & \(knx^{n-1}\)\tabularnewline
+  \hspace{6em} \(kx^n\) & \(knx^{n-1}\)\tabularnewline
   \(g(x) \pm h(x)\) & \(g^\prime (x) \pm h^\prime (x)\)\tabularnewline
   \(c\) & \(0\)\tabularnewline
   \({u \over v}\) &