The height of a right circular cylinder of maximum volume inscribed in a sphere of radius 3 is

If S₁ and S₂ are respectively the sets of local minimum and local maximum points of the function,

ƒ(x) = 9x⁴ + 12x³ – 36x² + 25, x $$ \in $$ R, then :

Let ƒ : [0, 2] $$ \to $$ R be a twice differentiable function such that ƒ''(x) > 0, for all x $$ \in $$ (0, 2). If $$\phi $$(x) = ƒ(x) + ƒ(2 – x), then $$\phi $$ is :

If the function f given by f(x) = x³ – 3(a – 2)x² + 3ax + 7, for some a$$ \in $$R is increasing in (0, 1] and decreasing in [1, 5), then a root of the equation, $${{f\left( x \right) - 14} \over {{{\left( {x - 1} \right)}^2}}} = 0\left( {x \ne 1} \right)$$ is :