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0

I guess what you are looking for is something like this scalefactor = 0.5; P[t_] = {t Sin[t], t^2/15}; curveplot[t0_] := ParametricPlot[P[t], {t, 0, t0}, PlotStyle -> Thickness[0.01], AxesLabel -> {"x", "y"}] vel[t_] = D[P[t], t]; velvector[t0_] := Graphics[{Red, Arrow[{P[t0], P[t0] + scalefactor vel[t0]}]}] Manipulate[Show[...


0

This is the answer: Maximize[x^3 + 2 x y, {x, y} ∈ Triangle[{{-4, -1}, {0, 3}, {4, -1}}]] Minimize[x^3 + 2 x y, {x, y} ∈ Triangle[{{-4, -1}, {0, 3}, {4, -1}}]]


7

You can use MeshFunctions to visualize the intersection. The following is one way to parametrize curve. f[x_, y_] := 2 x^3 - 5 y^4; p[x_, y_] := x + y + 5; expr = x /. Quiet[First@Solve[f[x, y] == p[x, y], {x, y}, Reals]]; t[u_] := expr /. y -> u; par[w_] := {t[w], w, p[t[w], w]}; p3D = Plot3D[{f[x, y], p[x, y]}, {x, -20, 20}, {y, -10, 10}, ...



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