`f(x) = (2x - 1)/(x^2)` 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 73 - 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)=(2x-1)/(x^2)`

Find the derivative of the function using the Quotient Rule. Set the derivative equal to zero to find the critical x value(s). When the derivative is equal to zero the tangent line will be horizontal to the graph of the function.

`f'(x)=[(x^2)(2)-(2x-1)(2x)]/x^4=0`

`2x^2-4x^2+2x=0` 

`-2x^2+2x=0`

`-2x(x-1)=0`

`x=0,x=1` 

Substitute the critical value(s) for x into the f(x) function to determine the point(s) at which the the graph of the function has a horizontal tangent line. 

x=0 is not a critical value because f(0) is undefined.

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

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

The graph of the function has a horizontal tangent line at the point (1, 1).

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