At $$x=0,$$ the function $$f\left( x \right) = {x^3} + 1$$ has

Consider the function $$f\left( x \right) = \left| x \right|$$ in the interval $$\,\, - 1 \le x \le 1.\,\,\,$$ At the point $$x=0, f(x)$$ is

The area enclosed between the straight line $$y=x$$ and the parabola $$y = {x^2}$$ in the $$x-y$$ plane is

The total derivative of the function $$'xy'$$ is