ClearAll["Global`*"]

stC[x_, k_] := 0.05  x^3 - 0.8  x^2 + (8 - k) x + 2  k^2

stC[x, k]

g[k_, tn_] := 
      Plot[stC[x, k], {x, 0, 20}, PlotRange -> {0, 100}, 
        PlotStyle -> Thickness[tn], AspectRatio -> 1, 
        PlotLabel -> {"\:77ed\:671f\:7dcf\:8cbb\:7528\:95a2\:6570 \
k=", k}, 
        AxesLabel -> {"x (\:751f\:7523\:91cf)", "STC(x,k)"}]

gx1 = g[0, 0.015]

gx2 = g[1.5, 0.01]

gx3 = g[3, 0.005]

Show[gx1, gx2, gx3, 
      PlotLabel -> "\:77ed\:671f\:7dcf\:8cbb\:7528\:95a2\:6570 \
k=0,1.5,3", 
      AxesLabel -> {"x (\:751f\:7523\:91cf)", "STC(x,k)"}]

tblstC1 = Table[stC[x, k], {k, 0, 3, 0.5}]

\(f1 = 
      Plot[Evaluate[tblstC1], {x, 0, 15}, PlotRange -> {0, 100}, 
        AspectRatio -> 1, 
        PlotLabel -> "短期総費用関数群(0≦k≦3)kを0.5ずつ増加", 
        AxesLabel -> {"x", "STC(x,k)"}]\)

tblstC2 = Table[stC[x, k], {k, 0, 3, 0.1}]

Plot[Evaluate[tblstC2], {x, 0, 15}, PlotRange -> {0, 100}, 
      AspectRatio -> 
        1, 
PlotLabel -> "\:77ed\:671f\:7dcf\:8cbb\
\:7528\:95a2\:6570\:7fa4(0≦k≦3)k\:30920.1\:305a\
\:3064\:5897\:52a0", 
      AxesLabel -> {"x", "STC(x,k)"}]

\( (*\ 
      k\ を\ 0\ から\ 3\ まで\ 0.5\ ずつ変化させたときの短期総費用関数の描画のアニメ - ション\ *) \)

\(Table[
      Plot[stC[x, k], {x, 0, 15}, PlotRange -> {0, 100}, 
        AspectRatio -> 1, 
        PlotLabel -> {"短期総費用関数 k=", k}, 
        AxesLabel -> {"x (生産量)", "STC(x,k)"}], {k, 0, 3, 0.5}]\)

D[stC[x, k], k] == 0

sol1 = Solve[D[stC[x, k], k] == 0, k][[1]]

ltC[x_] := Evaluate[stC[x, k] /. sol1]

Expand[ltC[x]]

f2 = 
      Plot[ltC[x], {x, 0, 15}, PlotRange -> {0, 100}, 
        PlotStyle -> {Thickness[0.02], RGBColor[0, 1, 0]}, 
        AspectRatio -> 1, 
        PlotLabel -> "\:9577\:671f\:7dcf\:8cbb\:7528\:95a2\:6570", 
        AxesLabel -> {"x (\:751f\:7523\:91cf)", "LTC(x)"}]

Show[f1, f2, 
      PlotLabel -> "\:77ed\:671f\:7dcf\:8cbb\:7528\:7fa4\:3068\:9577\
\:671f\:7dcf\:8cbb\:7528", 
      AxesLabel -> {"x", "STC(x,k), LTC(x)"}]

f3[k_] := 
      Plot[{stC[x, k], ltC[x]}, {x, 0, 15}, PlotRange -> {0, 100}, 
        PlotStyle -> {{Thickness[0.005], 
              RGBColor[0, 0, 0]}, {Thickness[0.01], RGBColor[0, 1, 0]}}, 
        AspectRatio -> 1, 
        PlotLabel -> {"\:77ed\:671f\:8cbb\:7528 k=", 
            k, "\:9577\:671f\:8cbb\:7528"}, 
        AxesLabel -> {"x", "STC(x,k),LTC(x)"}]

Table[f3[k], {k, 0, 3, 0.5}]