00:01
For this problem we're asked to find the points on the graph of f where the tangent line is horizontal.
00:04
So in other words, when does the tangent line have a slope of zero? and to find that we'll calculate the derivative of f, which tells us the slope, and then we'll set that equal to zero.
00:15
So to find f prime, we'll use the quotient rule to calculate that.
00:18
So i have the derivative of the top, which is just one, and then times the bottom, which is x squared plus one, and then minus the top times the derivative of the bottom.
00:30
Which is 2x.
00:31
All of this is over the bottom squared.
00:37
So i can simplify this.
00:38
I have negative x squared plus one.
00:43
This is all over still x squared plus one quantity squared.
00:48
And then i can actually factor the numerator.
00:50
So if i pull out a negative, then i have x minus one and then x plus one.
00:59
Again, this is all over x squared plus one quantity squared...