Tangent at a point $P_1$ (other than $(0,0)$ ) on the curve $y=x^3$ meets the curve again at $P_2$. The tangent at $P_2$ meets the curve at $\mathrm{P}_3$ and so on. Then the abscissae of $\mathrm{P}_1, \mathrm{P}_2, \mathrm{P}_3, \ldots, \mathrm{P}_{\mathrm{n}}$ form

The function $f(x)=2 x^3-3 x^2-12 x+4, x \in \mathbb{R}$ has

Let $\phi(x)=f(x)+f(2 a-x), x \in[0,2 a]$ and $f^{\prime \prime}(x)>0$ for all $x \in[0, a]$. Then $\phi(x)$ is