The maximum value of the function $f(x) = 3x^3 - 18x^2 + 27x - 40$ on the set $S = \{x \in R : x^2 + 30 \leq 11x\}$ is

Find two positive numbers $x$ and $y$ such that $x+y=60$ and $x y^{3}$ is maximum.

The curve $y = 2x^3 + ax^2 + bx + c$ passes through the origin,and the tangents at $x = -1$ and $x = 2$ are parallel to the $X$-axis. Then the values of $a, b,$ and $c$ are respectively:

On the interval $[0,1]$,the function $f(x) = x^{25}(1-x)^{75}$ takes its maximum value at the point

Let $f(x)=(x+3)^2(x-2)^3$ for $x \in [-4,4]$. If $M$ and $m$ are the maximum and minimum values of $f$ respectively in $[-4,4]$,then the value of $M-m$ is:

Consider the function $f(x) = x(x - 1)(x - 2) \dots (x - 100)$. Which one of the following is correct?