[Tex/LaTex] pgfplot: adjust legend style and add several paths

pgfplotsplot

I read the pgfplots manual the whole day, but unfortunately I am not able to achieve the following:

(1) legend style: make the legend-equation align left and modify the rectangular box to another shape (or best: remove the box)

(2) adding simple dashed lines, I tried to draw paths, but they don't appear were I want them to :/ e.g. from x=7 to the intersection of two curves.

\documentclass[13pt,a4paper,headlines=6,headinclude=true]{scrartcl}
\usepackage{tikz,pgfplots}
\usepackage{amsmath,amssymb,stmaryrd}
\begin{document}

  \begin{tikzpicture}[scale=1]
      \begin{axis}[axis lines=middle,xmin=-5,xmax=16,ymin=2,ymax=299,
        extra x ticks={0,4,7},
        tick label style={font=\tiny}, 
        legend style={font=\tiny,legend pos=outer north east}
            ]
            \addplot+[no marks,blue,domain=0.2:10,samples=150, thick] {(x)^3 - 12*(x)^2 + 60*x+98};
        \addlegendentry{$C(x) = x^3 - 12x^2 + 60x+98$};
            \addplot+[no marks,red,domain=0.2:13,samples=150, thick] {3*(x)^2 - 24*x + 60};
            \addlegendentry{$MC(x)=3x^2 - 24x + 60$};
            \addplot+[no marks,orange,domain=0.2:13,samples=150, thick] {(x)^2 - 12*x + 60 + (98)/(x)};
            \addlegendentry{$AV(x)=x^2 - 12x + 60 + \frac{98}{x}$};
            \path[draw=gray, dashed] (4,2) -- (4,50); 
            \path[draw=gray, dashed] (10,-2) -- (10,50); 
      \end{axis}
    \end{tikzpicture}

\end{document}

enter image description here

I would appreciate any further remarks on how to make this look nicer. Thank you very much.

Best Answer

For removing the box, use draw=none and for aligning equations to the l;eft, use cells={anchor=west} in

legend style={draw=none,font=\tiny,legend pos=outer north east,cells={anchor=west}}

Further, you need to add `\pgfplotsset{compat=1.12} in order to use 

\path[draw=gray, dashed] (10,-2) -- (10,50);

otherwise, you may have to use 

\path[draw=gray, dashed] (axis cs:10,-2) -- (axis cs:10,50);

Code:

\documentclass[13pt,a4paper,headlines=6,headinclude=true]{scrartcl}
\usepackage{pgfplots}
\pgfplotsset{compat=1.12}
\begin{document}

  \begin{tikzpicture}[scale=1]
      \begin{axis}[axis lines=middle,xmin=-5,xmax=16,ymin=2,ymax=299,
        extra x ticks={0,4,7},
        tick label style={font=\tiny},
        legend style={draw=none,font=\tiny,legend pos=outer north east,cells={anchor=west}}
            ]
            \addplot+[no marks,blue,domain=0.2:10,samples=150, thick] {(x)^3 - 12*(x)^2 + 60*x+98};
        \addlegendentry{$C(x) = x^3 - 12x^2 + 60x+98$};
            \addplot+[no marks,red,domain=0.2:13,samples=150, thick] {3*(x)^2 - 24*x + 60};
            \addlegendentry{$MC(x)=3x^2 - 24x + 60$};
            \addplot+[no marks,orange,domain=0.2:13,samples=150, thick] {(x)^2 - 12*x + 60 + (98)/(x)};
            \addlegendentry{$AV(x)=x^2 - 12x + 60 + \frac{98}{x}$};
            \path[draw=gray, dashed] (4,2) -- (4,50);
            \path[draw=gray, dashed] (10,-2) -- (10,50);
      \end{axis}
    \end{tikzpicture}

\end{document}

enter image description here

To change the shape, use usetikzlibrary{shapes.geometric} (for example) and then

legend style={ellipse,fill=olive,font=\tiny,legend pos=outer north east,cells={anchor=west}}

gives (ugly)

enter image description here

With

legend style={rounded corners,fill=olive!40,font=\tiny,legend pos=outer north east,cells={anchor=west}}

we get

enter image description here

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