[math] \newcommand{\ex}[1]{\item } \newcommand{\sx}{\item} \newcommand{\x}{\sx} \newcommand{\sxlab}[1]{} \newcommand{\xlab}{\sxlab} \newcommand{\prov}[1] {\quad #1} \newcommand{\provx}[1] {\quad \mbox{#1}} \newcommand{\intext}[1]{\quad \mbox{#1} \quad} \newcommand{\R}{\mathrm{\bf R}} \newcommand{\Q}{\mathrm{\bf Q}} \newcommand{\Z}{\mathrm{\bf Z}} \newcommand{\C}{\mathrm{\bf C}} \newcommand{\dt}{\textbf} \newcommand{\goesto}{\rightarrow} \newcommand{\ddxof}[1]{\frac{d #1}{d x}} \newcommand{\ddx}{\frac{d}{dx}} \newcommand{\ddt}{\frac{d}{dt}} \newcommand{\dydx}{\ddxof y} \newcommand{\nxder}[3]{\frac{d^{#1}{#2}}{d{#3}^{#1}}} \newcommand{\deriv}[2]{\frac{d^{#1}{#2}}{dx^{#1}}} \newcommand{\dist}{\mathrm{distance}} \newcommand{\arccot}{\mathrm{arccot\:}} \newcommand{\arccsc}{\mathrm{arccsc\:}} \newcommand{\arcsec}{\mathrm{arcsec\:}} \newcommand{\arctanh}{\mathrm{arctanh\:}} \newcommand{\arcsinh}{\mathrm{arcsinh\:}} \newcommand{\arccosh}{\mathrm{arccosh\:}} \newcommand{\sech}{\mathrm{sech\:}} \newcommand{\csch}{\mathrm{csch\:}} \newcommand{\conj}[1]{\overline{#1}} \newcommand{\mathds}{\mathbb} [/math]

Sketch the graph of each of the following functions, carefully labeling all extreme points and all points of inflection. Classify each extreme point as to type.

• [math]x^2 - 5x + 6[/math]
• [math]3 - 2x - x^2[/math]
• [math]2x^2 - 3x - 1[/math]
• [math]5-2x^2[/math]
• [math]x^3 - 3x[/math]
• [math](x+1)(x^3 - x^2 - 5x + 13)[/math]
• [math]\frac{x+2}x[/math]
• [math]\frac{16}x + x^2[/math]
• [math]x^3 - x[/math]
• [math]x^4 - x[/math]
• [math](a^\frac23 - x^\frac23)^\frac32[/math]
• [math]|x|[/math]
• [math]|x-7|[/math]
• [math]3 + \frac6{x-2}[/math]
• [math]x^4 - 8x^2 + 3[/math]
• [math]\frac{x^2 - 5x + 4}{8x}[/math]
• [math](x-1)(x-2)(x-3)[/math]
• [math]1+6x - \frac12x^3[/math].