Calculus of a Single Variable, Chapter 2, 2.3, Section 2.3, Problem 76

Given: f(x)=(x-4)/(x^2-7)
Find the derivative of the function using the Quotient Rule. Set the derivative equal to zero and solve for the critical x value(s). When the derivative is zero the slope of the tangent line will be horizontal to the graph.
f'(x)=[(x^2-7)(1)-(x-4)(2x)]/(x^2-7)^2=0
(x^2-7-2x^2+8x)=0
-x^2+8x-7=0
x^2-8x+7=0
(x-1)(x-7)=0
x=1,x=7
Plug in the critical values for x into the f(x) equation.
f(x)=(x-4)/(x^2-7)
f(1)=(1-4)/(1^2-7)=-3/-6=1/2
f(7)=(7-4)/(7^2-7)=3/42=1/14
The tangent line will be horizontal to the graph at points (1,1/2) and (7,1/14).