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A function $f: \mathbb{R} \rightarrow \mathbb{R}$ is convex if for $x, y \in \mathbb{R}, \alpha \in[0,1], f(\alpha x+(1-\alpha) y) \leq \alpha f(x)+(1-\alpha) f(y)$.

Which of the following is not convex:

  1. $x^{2}$
  2. $x^{3}$
  3. $x$
  4. $x^{4}$
  5. $\mathrm{e}^{x}$

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