The maximum value attained by the function $$f(x)=x(x-1) (x-2)$$ in the interval $$\left[ {1,2} \right]$$ is _________.

A particle, starting from origin at $$t=0$$ $$s,$$ is traveling along $$x$$-axis with velocity $$v = {\pi \over 2}\cos \left( {{\pi \over 2}t} \right)m/s$$
At $$t=3$$ $$s,$$ the difference between the distance covered by the particle and the magnitude of displacement from the origin is _________.

Minimum of the real valued function $$f\left( x \right) = {\left( {x - 1} \right)^{2/3}}$$ occurs at $$x$$ equal to

Let $$f\left( x \right) = x{e^{ - x}}.$$ The maximum value of the function in the interval $$\left( {0,\infty } \right)$$ is