What is the nature of the function $$f(x)=x^3-3 x^2+4 x$$ on real numbers?

The side of an equilateral triangle expands at the rate of $$\sqrt{3} \mathrm{~cm} / \mathrm{sec}$$. When the side is $$12 \mathrm{~cm}$$, the rate of increase of its area is

If $$f(x)=2 x^3+9 x^2+\lambda x+20$$ is a decreasing function of $$x$$ in the largest possible interval $$(-2,-1)$$, then $$\lambda$$ is equal to

$$ \text { The point on the curve } x^2=x y \text { which is closest to }(0,5) \text { is } $$