plot - Highlighting intersection points of 2 functions (Mathematica) -


given 2 functions, need find intersection points , show them on graph. particular problem, functions are: f(x) = - (x - 2) ^ 2, g(x) = x/(x+1).

so far, have following:
plot[{-(x - 2)^2 + 4, x/(x + 1)}, {x, 0, 4}, filling -> {1 -> {{2}, {white, lightblue}}}]
nsolve[-(x - 2)^2 + 4 == x/(x + 1), {x, y}]

but have no idea how show points on graph. how do that?

you can use epilog option add graphics primitives plot:

intersections = {x, y} /.     nsolve[y == -(x - 2)^2 + 4 && y == x/(x + 1), {x, y}];  plot[{-(x - 2)^2 + 4, x/(x + 1)}, {x, 0, 4},   filling -> {1 -> {{2}, {white, lightblue}}},   epilog -> {red, point[intersections]}]

enter image description here


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