Calculus of a Single Variable, Chapter 2, 2.3, Section 2.3, Problem 73

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).