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Editorial Team
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Asked: 2026-05-27T16:23:39+00:00

I asked this question yesterday but not sure if I made clear what I

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I asked this question yesterday but not sure if I made clear what I was looking for. Say I have two curves defined as f[x_]:=... and g[x_]:=... as shown below. I want to use Mathematica to determine the abscissa intersection of the tangent to both curves and store value for each curve separately. Perhaps this is really a trivial task, but I do appreciate the help. I am an intermediate with Mathematica but this is one I haven’t been able to find a solution to elsewhere.

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1 Answer

  1. Editorial Team
    f[x_] := x^2
g[x_] := (x - 2)^2 + 3

sol = Solve[(f[x1] - g[x2])/(x1 - x2) == f'[x1] == g'[x2], {x1, x2}, Reals]

(* ==> {{x1 -> 3/4, x2 -> 11/4}} *)

eqns = FlattenAt[{f[x], g[x], f'[x1] x + g[x2] - f'[x1] x2 /. sol}, 3]; 
Plot[eqns, {x, -2, 4}, Frame -> True, Axes -> None]

    enter image description here

    Please note that there will be many functions f and g for which you won’t find a solution in this way. In that case you will have to resort to numerical problem solving methods.

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