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   "source": [
    "# Exercises on Fixed Point Iteration"
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   "source": [
    "## Exercise 1\n",
    "\n",
    "The equation\n",
    "$x^3 -2x + 1 = 0$\n",
    "can be written as a fixed point equation in many ways, including\n",
    "1. $\\displaystyle x = \\frac{x^3 + 1}{2}$\n",
    "<br>\n",
    "and\n",
    "2. $x = \\sqrt[3]{2x-1}$\n",
    "\n",
    "For each of these options:\n",
    "\n",
    "(a) Verify that its fixed points do in fact solve the above cubic equation.\n",
    "\n",
    "(b) Determine whether fixed point iteration with it will converge to the solution $r=1$.\n",
    "(assuming a \"good enough\" initial approximation).\n",
    "\n",
    "**Note:** computational experiments can be a useful start, but prove your answers mathematically!"
   ]
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    "---\n",
    "This work is licensed under [Creative Commons Attribution-ShareAlike 4.0 International](https://creativecommons.org/licenses/by-sa/4.0/)"
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