Problems
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- Prove $f(x)=\frac{1}{x}$ is concave down on the open interval $(-\infty,0)$ and concave up on the open interval $(0,\infty)$.
- Prove that $f(x)=x$ has no concavity.
- Prove $x^3$ is concave down on the interval $(-\infty,0)$ and concave up on the interval $(0,\infty)$.
- Prove that $f(x)=x^2$ is concave up.
