_Root Finding Homework Problem - An Introduction to Optimization for Engineers.ipynb

{
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   "metadata": {},
   "outputs": [],
   "source": [
    "using Plots"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {},
   "outputs": [
    {
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       "  ⋮\n",
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     "execution_count": 92,
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     "output_type": "execute_result"
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   "source": [
    "x = LinRange(-pi, 4*pi, 401)\n",
    "f = sin.(x) - ((x.^2)/10) + x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {},
   "outputs": [
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      ]
     },
     "execution_count": 93,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plot(x,f)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "zeroth_derivative (generic function with 1 method)"
      ]
     },
     "execution_count": 94,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function zeroth_derivative(x)\n",
    "    \n",
    "    return sin(x) + x - (x^2)/10\n",
    "    \n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "first_derivative (generic function with 1 method)"
      ]
     },
     "execution_count": 95,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function first_derivative(x)\n",
    "    \n",
    "    return cos(x) + 1 - (x/5)\n",
    "\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "second_derivative (generic function with 1 method)"
      ]
     },
     "execution_count": 96,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "function second_derivative(x)\n",
    "    \n",
    "    return -sin(x)-(1/5)\n",
    "    \n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = 8\n",
    "maximum_iterations = 10\n",
    "\n",
    "for iteration = 1:maximum_iterations\n",
    "    \n",
    "    x = x - (zeroth_derivative(x)/first_derivative(x))\n",
    "    \n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "9.71011541530111"
      ]
     },
     "execution_count": 98,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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