The function $f(x)=2|x|+|x+2|-||x+2|-2|x||$ has a local minimum or a local maximum at $x=$

Divide $20$ into two parts such that the product of one part and the cube of the other is maximum. The two parts are

The function $f(x)=x^3+a x^2+b x+c$ with $a^2 \leq 3 b$ has:

If $P(x) = a_0 + a_1x^2 + a_2x^4 + \dots + a_nx^{2n}$ is a polynomial in $x \in R$ with $0 < a_1 < a_2 < \dots < a_n$,then what does $P(x)$ have?

What is the local maximum value of $\frac{\log x}{x}$?

If $x_0$ is the point of local minima of $f(x) = \bar{a} \cdot (\bar{b} \times \bar{c})$ where $\bar{a} = x \hat{i} - 2 \hat{j} + 3 \hat{k}$,$\bar{b} = -2 \hat{i} + x \hat{j} - \hat{k}$,$\bar{c} = 7 \hat{i} - 2 \hat{j} + x \hat{k}$,then the value of $\bar{a} \cdot \bar{b}$ at $x = x_0$ is