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

Textbook Question

Chapter 2, 2.3 - Problem 75 - Calculus of a Single Variable (10th Edition, Ron Larson).
See all solutions for this textbook.

1 Answer | Add Yours

mathace's profile pic

mathace | (Level 3) Assistant Educator

Posted on

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.

`f'(x)=[(x-1)(2x)-x^2(1)]/(x-1)^2`

`f'(x)=(2x^2-2x-x^2)/(x-1)^1=0`

`f'(x)=x^2-2x=0`

`x(x-2)=0`

`x=0,x=2` 

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

`f(x)=x^2/(x-1)`

`f(0)=0^2/(0-1)=0`

` ` `f(2)=2^2/(2-1)=4` 

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

We’ve answered 318,989 questions. We can answer yours, too.

Ask a question