The length of a longest interval in which the function $$3\,\sin x - 4{\sin ^3}x$$ is increasing, is

The point(s) in the curve $${y^3} + 3{x^2} = 12y$$ where the tangent is vertical, is (are)

The triangle formed by the tangent to the curve $$f\left( x \right) = {x^2} + bx - b$$ at the point $$(1, 1)$$ and the coordinate axex, lies in the first quadrant. If its area is $$2$$, then the value of $$b$$ is

If $$f\left( x \right) = x{e^{x\left( {1 - x} \right)}},$$ then $$f(x)$$ is