`f(x) = (x^2)/(x - 1)` Determine the point(s) at which the graph of the function has a horizontal tangent line.

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Chapter 2, 2.3 - Problem 75 - Calculus of a Single Variable (10th Edition, Ron Larson).
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mathace | (Level 3) Assistant Educator

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Given `f(x)=x^2/(x-1)`

Find the derivative of the function using the Quotient Rule. Set the derivative equal to 0 and solve for the x value(s). When the derivative is equal to zero, the slope of the tangent line is horizontal to the graph.






Plug in the critical x value(s) into the original function.



` ` `f(2)=2^2/(2-1)=4` 

The function will have horizontal lines at the points (0,0) and (2,4).

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