The stationary points of the curve $y = 8x^2 - x^4 - 4$ are . . . . . .

The maximum value of the function $f(x)=2x^3-15x^2+36x-48$ on the set $A=\{x | x^2+20 \leq 9x\}$ is

The maximum value of the function $f(x) = -|x+1| + 3, x \in R$ is . . . . . . .

The minimum value of the function $f(x) = 3x^4 - 8x^3 + 12x^2 - 48x + 25$ on the interval $[0, 3]$ is equal to:

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:

If the function $f(x)=xe^{-x}, x \in R$ attains its maximum value $\beta$ at $x=\alpha$, then $(\alpha, \beta)=$