Maximum slope of the curve $y = -x^3 + 3x^2 + 9x - 27$ is

What is the maximum slope of the curve $y = -x^3 + 3x^2 + 9x - 27$?

If $f(x)$ is a non-zero polynomial of degree four,having local extreme points at $x = -1, 0, 1$; then the set $S = \{x \in R; f(x) = f(0)\}$ contains exactly

$A$ poster is to be printed on a rectangular sheet of paper of area $18 \ m^2$. The margins at the top and bottom of $75 \ cm$ each and at the sides $50 \ cm$ each are to be left. Then the dimensions,i.e.,height and breadth of the sheet,so that the space available for printing is maximum,are respectively:

In the interval $[0, 2\pi]$,the slope of the tangent to the function $f(x) = e^x \sin x$ is maximum at $x = \dots$

The function $f(x) = x^2 + \frac{54}{x}$