If $x + y = 10$,then the maximum value of $xy$ is

The maximum value of $f(x) = \frac{x}{4 + x + x^2}$ on the interval $[-1, 1]$ is:

$A(1,15), B(3,-12), C(6,12)$ are three consecutive turning points of a continuous curve $y=f(x)$. If $f(x)=0$ only for $x=\alpha$ and $x=\beta$,then $|\beta-\alpha| < $

The absolute minimum value of the function $f(x) = |x^2 - x + 1| + [x^2 - x + 1]$,where $[t]$ denotes the greatest integer function,in the interval $[-1, 2]$,is:

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

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