If $$y = \left| x \right|$$ for $$x < 0$$ and $$y=x$$ for $$x \ge 0$$ then

The function $$f\left( x \right) = {x^3} - 6{x^2} + 9x + 25$$ has

The function $$f\left( x \right) = \left| {x + 1} \right|$$ on the interval $$\left[ { - 2,0} \right]$$ is __________.

The value of $$\varepsilon $$ in the mean value theoram of $$f\left( b \right) - f\left( a \right) = \left( {b - a} \right)\,\,f'\left( \varepsilon \right)$$ for $$f\left( x \right) = A{x^2} + Bx + C$$ in $$(a, b)$$ is