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Please help: Determine the points at which the graph of the function has a horizontal tangent line.

Please help: Determine the points at which the graph of the function has a horizontal-example-1
User Ciaran Fisher
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1 Answer

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\\ \tt\hookrightarrow f(x)=(x^2)/(x-6)

Find inverse


\\ \tt\hookrightarrow y=(x^2)/(x-6)


\\ \tt\hookrightarrow x=(x^2+6y)/(y)


\\ \tt\hookrightarrow f'(x)=(x^2+6x)/(x)=x+6

Now


\\ \tt\hookrightarrow x+6=0\implies x=-6

Find Horizontal tangency


\\ \tt\hookrightarrow f(6)=((-6)^2)/(-6-6)


\\ \tt\hookrightarrow f(6)=(36)/(-12)=-3

So

  • (x,y) =(-6,-3)
User Mech
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