`f(x) = (x - 4)/(x^2 - 7)` 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 76 - 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-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.







Plug in the critical values for x into the f(x) equation.




The tangent line will be horizontal to the graph at points `(1,1/2)`  and `(7,1/14).`


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