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Consider \(f(x) = x\ln(4 - x^2)\), with \(-2 < x < 2\).

Part of the graph of \(f\) is shown below.

Let \(P\) and \(Q\) be the points on the curve of \(f\) where the tangent to the graph of \(f\) is parallel to the x-axis.

1. 1. Find the x-coordinates of \(P\) and \(Q\).

   2. Consider \(f(x) = k\).

      State all values of \(k\) for which there are exactly two solutions.

Let \(g(x) = x^3\ln(4 - x^2)\), with \(-2 < x < 2\).

2. Show that \(g^\prime(x)=\frac{-2x^4}{4 - x^2} + 3x^2\ln(4 - x^2)\).

3. Sketch the graph of \(g^\prime\).

4. Consider \(g^\prime(x) = w\).

   State all values of \(w\) for which there are exactly two solutions.