[tex]\bf y=x^3-6x^2-34x-9\implies \cfrac{dy}{dx}=3x^2-12x-34
\\\\\\
\stackrel{\textit{slope of 2}}{2}=3x^2-12x-34\implies 0=3x^2-12x-36
\\\\\\
0=x^2-4x-12\implies 0=(x-6)(x+2)\implies x=
\begin{cases}
6\\
-2
\end{cases}\\\\
-------------------------------\\\\
\stackrel{y}{f(6)}=(6)^3-6(6)^2-34(6)-9\implies f(6)=-213\\\\\\ (\stackrel{x}{6}~,~\stackrel{y}{-213})
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\stackrel{y}{f(-2)}=(-2)^3-6(-2)^2-34(-2)-9\implies f(-2)=27\\\\\\ (\stackrel{x}{-2}~,~\stackrel{y}{27})[/tex]
