[tex]\\ \tt\hookrightarrow f(x)=\dfrac{x^2}{x-6}[/tex]
Find inverse
[tex]\\ \tt\hookrightarrow y=\dfrac{x^2}{x-6}[/tex]
[tex]\\ \tt\hookrightarrow x=\dfrac{x^2+6y}{y}[/tex]
[tex]\\ \tt\hookrightarrow f'(x)=\dfrac{x^2+6x}{x}=x+6[/tex]
Now
[tex]\\ \tt\hookrightarrow x+6=0\implies x=-6[/tex]
Find Horizontal tangency
[tex]\\ \tt\hookrightarrow f(6)=\dfrac{(-6)^2}{-6-6}[/tex]
[tex]\\ \tt\hookrightarrow f(6)=\dfrac{36}{-12}=-3[/tex]
So
