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Let \(f\) be the function defined and twice differentiable on \(\mathbb{R}\) by:$$ f(x) = (x^2 + 1)e^x $$
  1. Calculate \(f'(x)\) and deduce the variations of \(f\) on \(\mathbb{R}\).
    1. Calculate the second derivative \(f''(x)\).
    2. Study the sign of \(f''(x)\) and deduce the coordinates of any points of inflection on the graph of \(f\).

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