Can you find... chain rule edition

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Can you find …

1. … functions \(f(x)\) and \(g(x)\) so that \(f(g(x))\) has stationary points when \(x=-1\) and \(x=5\)?

2. … a function \(g(x)\) so that \(\ln{g(x)}\) has a local minimum?

3. … functions \(f(x)\) and \(g(x)\) so that \(f(g(x))\) has no stationary points?