The abscissa of the points,where the tangent to the curve $y=x^3-3x^2-9x+5$ is parallel to the $X$-axis,are

If $x + 2y = 8$,then the maximum value of $xy$ is .......

The condition that $f(x) = ax^3 + bx^2 + cx + d$ has no extreme value is

If the function $f$ is given by $f(x)=x^3-3(a-2)x^2+3ax+7$,for some $a \in R$,is increasing in $(0,1]$ and decreasing in $[1,5)$,then a root of the equation $\frac{f(x)-14}{(x-1)^2}=0$ $(x \neq 1)$ is

The sum of the lengths of the hypotenuse and one side of a right-angled triangle is constant. The area of the triangle will be maximum if the angle between them is:

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