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Consider a function \(f(x)\). The line \(L_1\) with equation \(y = 3x + 1\) is tangent to the graph of \(f(x)\) at \(x = 2\).

1. 1. Write down \(f^\prime(2)\).
   2. Find \(f(2)\).

Let \(g(x) = f(x^2 + 1)\) and let \(P\) be the point on the graph of \(g\) where \(x = 1\).

2. Show that the graph of \(g\) has a slope of 6 at point \(P\).

Let \(L_2\) be the tangent to the graph of \(g\) at point \(P\). \(L_1\) intersects \(L_2\) at point \(Q\).

3. Find the y-coordinate of \(Q\).