If the curves $$y=x^3-3 x^2-8 x-4$$ and $$y=3 x^2+7 x+4$$ touch each other at a point $$P$$, then the equation of common tangent at $$P$$ is

The maximum value of $$f(x)=\frac{x}{1+4 x+x^2}$$ is

The minimum value of $$f(x)=x+\frac{4}{x+2}$$ is

The condition that $$f(x)=a x^3+b x^2+c x+d$$ has no extreme value is