For the curve $y = x e^x$,the point:

The maximum value of $xy$ subject to $x+y=7$ is

$A$ triangular garden is fenced on two sides,and the third side is a straight river bank. The two fenced sides have an equal length of $x$. What is the maximum area that can be enclosed by the garden?

If $m$ and $M$ are respectively the absolute minimum and absolute maximum values of a function $f(x)=2x^3+9x^2+12x+1$ defined on $[-3,0]$, then $m+M=$

The minimum value of the function $f(x)=2|x-1|+|x-2|$ is

Let a function $f(x)$ be continuous in an interval $[a, b]$. Let $\delta > 0$ be a very small real number. Let $c \in (a, b)$ be such that $f(c - \delta) < f(c)$ and $f(c + \delta) < f(c)$ for every $\delta > 0$. Let $(f(\alpha - \delta) - f(\alpha))(f(\alpha + \delta) - f(\alpha)) < 0$ for all $\alpha \in (a, b)$ and $\alpha \neq c$. Then: