Mathematica 代码生成函数单调性分析表格

range = {0, 1}; f[x_] := x^2 - x + 1; fD[x_] := D[f[x], x]; fDpos = fD[x] > 0 /. x -> # & /@ range; fDzero = fD[x] == 0 /. x -> # & /@ range; fDneg = fD[x] < 0 /. x -> # & /@ range; fmono = {f[x], f[x]} & /@ ({x}~Join~Solve[D[f[t], t] == 0, t]); fmax = MaximalBy[fmono, First][[1, 1]]; fmin = MinimalBy[fmono, First][[1, 1]]; Grid[{{'x', range[[1]], '-', range[[2]]}, {'f'(x)', fDpos[[1]], fDzero[[1]], fDneg[[1]]}, {'f(x)', If[fmax == fmin, '常数', '极大值'], If[fmax == fmin, '', '极小值'], If[fmono[[1, 2]] == '增', '[UpperRightArrow]', '[LowerRightArrow]']}}, Alignment -> {{Center, '.'}}, Frame -> All]