this is a simple example to ask: is this the style of plot your looking to do? (swokowsi calc. 5th ed p. 880). Let C denote first-octant arc of the curve in which the parabaloid 2z=16-x^2-y^2 and the plane x+y=4 intersect. (describe minima and maxima of C) (note plotting those with Opacity[] would be easier!)
Remove[x, y, z, t, xt, yt, zt, g1, g5];
g1 = Plot3D[
If[1/2 (16 - x^2 - y^2) > 0, 1/2 (16 - x^2 - y^2), Null], {x, -4,
4}, {y, -4, 4}, Mesh -> False, PlotPoints -> 50];
x =.; y =.; z =.; t =.;
xt[t_] := 4 - t;
yt[t_] := t;
zt[t_] := 4 t - t^2;
g5 = ParametricPlot3D[{xt[t], yt[t], zt[t]}, {t, 0, 4}]
Show[g5, g1, ViewPoint -> {1.3 - 1, 2.4, 2.0 - 2.25},
PlotRange -> {{-4, 4}, {-4, 4}, {0, 8}}]
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