Update lab06.ipynb

added 1/2  to the g''(a) term of the taylor expansion of g(x)

Author: kthood

book/labs/1_Color_Labs/5_Edge_Detection/lab06.ipynb

@@ -266,8 +266,8 @@
     "which is the same symmetric difference formula you've seen before.\n",
     "To approximate the second derivative $g''(a)$, use the estimations\n",
     "\\begin{align*}\n",
-    "    g(a+h) &\\approx g(a) + \\frac{g'(a)}{1}((a+h)-a) + \\frac{g''(a)}{1\\cdot 2}((a+h)-a)^2 = g(a) + g'(a)h + g''(a)h^2 \\\\ \n",
-    "    g(a-h) &\\approx g(a) + \\frac{g'(a)}{1}((a-h)-a) + \\frac{g''(a)}{1\\cdot 2}((a-h)-a)^2 = g(a) - g'(a)h + g''(a)h^2. \\\\ \n",
+    "    g(a+h) &\\approx g(a) + \\frac{g'(a)}{1}((a+h)-a) + \\frac{g''(a)}{1\\cdot 2}((a+h)-a)^2 = g(a) + g'(a)h + \\frac{1}{2} g''(a)h^2 \\\\ \n",
+    "    g(a-h) &\\approx g(a) + \\frac{g'(a)}{1}((a-h)-a) + \\frac{g''(a)}{1\\cdot 2}((a-h)-a)^2 = g(a) - g'(a)h + \\frac{1}{2} g''(a)h^2. \\\\ \n",
     "\\end{align*}\n",
     "    \n",
     "<br>"