00:01
So i'm given a function f of x, and that's x plus 7 over x minus 7.
00:06
I want to find the point on the graph or the slope of the tangent line.
00:11
I believe that says negative 7 over 2.
00:14
The numerator is cut off.
00:16
So to do that, i'm going to find the derivative of that function using quotient rule.
00:22
So denominator times derivative of the numerator minus the numerator times the derivative of the denominator, over the denominator squared.
00:34
I'm going to clean that up.
00:35
So i have x minus 7 minus 6 minus 7 over x minus 7 squared.
00:44
And then you can say that my x and negative x cancel.
00:49
I'm going to have negative 14 over x minus 7 squared.
00:54
Now i'm going to set that derivative equal to negative 7 over 2.
01:03
And to solve, i'm going to cross multiply...