Find Horizontal Tangent Line of f(x) = (x-4)/(x^2-7)

[ashleyrc]

Homework Statement

determine where the graph of the function f(x) = (x-4)/(x^2-7) has a horizontal tangent line.

Homework Equations

used quotient rule. factored and simplified

The Attempt at a Solution

came up with ((x^2-7)-(2x^2-8x))/(x^2-7)^2
then set to 0, and came up with -x^2-8x-7=0
then to find the points where the graph has a horizontal tan line, i came up with 2 situations: -(x+7)(x+1) = -7, -1; or (-x-7)(x+1) = 7, -1. which one is right, and did i do the rest of it correctly/

 

[sutupidmath]

Have you learned limits? And do you have any rough idea how the equation of a horizontal tangent line looks like?

 

[ashleyrc]

yeah, i have learned limits, and I'm going to guess a horizontal tangent line is located wherever the slope is 0. i have seen too many of those equations though.

 

[sutupidmath]

ok then since you know what limits are, it makes life much easier.

Then somewhere you might have learned that a function has a horizontl line if any of the following is the case

$$\lim_{x\rightarrow- \infty}f(x)=a;\lim_{x\rightarrow \infty}f(x)=a$$ where a is any constant, and f is your given function.

then y=a is your horizontal tangent line.