{
 "metadata": {
  "name": ""
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from __future__ import division\n",
      "\n",
      "# ^^^ Demo will not work without this.\n",
      "\n",
      "import numpy as np\n",
      "import matplotlib.pyplot as pt"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 13
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "a = 2\n",
      "b = 6\n",
      "\n",
      "x = np.linspace(a, b)\n",
      "\n",
      "def f(x):\n",
      "    return 1e-2 * np.exp(x) - 2\n",
      "\n",
      "pt.grid()\n",
      "pt.plot(x, f(x))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 14,
       "text": [
        "[<matplotlib.lines.Line2D at 0x312ca90>]"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": "iVBORw0KGgoAAAANSUhEUgAAAX4AAAEACAYAAAC08h1NAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x33b2e50>"
       ]
      }
     ],
     "prompt_number": 14
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# Run this cell in-place many times. (Ctrl-Enter)\n",
      "\n",
      "m = a + (b-a)/2\n",
      "\n",
      "if np.sign(f(a)) == np.sign(f(m)):\n",
      "    ...\n",
      "else:\n",
      "    ...\n",
      "    \n",
      "print a, b"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "5.29831695557 5.29831886292\n"
       ]
      }
     ],
     "prompt_number": 49
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<!--\n",
      "if np.sign(f(a)) == np.sign(f(m)):\n",
      "    a = m\n",
      "else:\n",
      "    b = m\n",
      "-->\n",
      "(Edit this cell for solution.)"
     ]
    }
   ],
   "metadata": {}
  }
 ]
}