{"version":9,"randomSeed":"86707fb993b5b08800ee09111235b8ec","graph":{"viewport":{"xmin":-0.3938799162141787,"ymin":-0.20293243934826677,"xmax":4.312002436726996,"ymax":2.764771463973979}},"expressions":{"list":[{"type":"folder","id":"2","title":"functions"},{"type":"text","id":"5","folderId":"2","text":"function for which to find extremum"},{"type":"expression","id":"3","folderId":"2","color":"#2d70b3","latex":"f\\left(x\\right)=\\sin x"},{"type":"text","id":"21","folderId":"2","text":"select new x-values (two-element list) for a bisection"},{"type":"text","id":"37","folderId":"2","text":"change sign of comparison to switch between finding maxima/minima"},{"type":"expression","id":"22","folderId":"2","color":"#388c46","latex":"N\\left(X\\right)=\\left\\{f\\left(X\\left[1\\right]\\right)>f\\left(X\\left[2\\right]\\right):\\left[X\\left[1\\right],\\frac{X\\left[1\\right]+X\\left[2\\right]}{2}\\right],\\left[\\frac{X\\left[1\\right]+X\\left[2\\right]}{2},X\\left[2\\right]\\right]\\right\\}"},{"type":"folder","id":"7","title":"step 0-3"},{"type":"expression","id":"23","folderId":"7","color":"#6042a6","latex":"X_{0}=\\left[1,5\\right]"},{"type":"expression","id":"26","folderId":"7","color":"#2d70b3","latex":"X_{1}=N\\left(X_{0}\\right)"},{"type":"expression","id":"28","folderId":"7","color":"#6042a6","latex":"X_{2}=N\\left(X_{1}\\right)"},{"type":"expression","id":"29","folderId":"7","color":"#000000","latex":"X_{3}=N\\left(X_{2}\\right)"},{"type":"expression","id":"25","folderId":"7","color":"#c74440","latex":"\\left(\\operatorname{join}\\left(X_{0},X_{1},X_{2},X_{3}\\right),f\\left(\\operatorname{join}\\left(X_{0},X_{1},X_{2},X_{3}\\right)\\right)\\right)"},{"type":"folder","id":"15","title":"step 4-7"},{"type":"expression","id":"31","folderId":"15","color":"#2d70b3","latex":"X_{4}=N\\left(X_{3}\\right)"},{"type":"expression","id":"32","folderId":"15","color":"#388c46","latex":"X_{5}=N\\left(X_{4}\\right)"},{"type":"expression","id":"33","folderId":"15","color":"#6042a6","latex":"X_{6}=N\\left(X_{5}\\right)"},{"type":"expression","id":"34","folderId":"15","color":"#000000","latex":"X_{7}=N\\left(X_{6}\\right)"},{"type":"expression","id":"35","folderId":"15","color":"#c74440","latex":"\\left(\\operatorname{join}\\left(X_{4},X_{5},X_{6},X_{7}\\right),f\\left(\\operatorname{join}\\left(X_{4},X_{5},X_{6},X_{7}\\right)\\right)\\right)"}]}}