00:01
In this question, we are asked to find the points at which the graph has the horizontal tangent line.
00:07
And to do that, the tangent line is horizontal if f prime of x equals to 0.
00:20
F prime of x by the quotient rule equals to the derivative of the numerator multiplied by the denominator minus the numerator multiplied by the derivative of the denominator divided by the square of the denominator.
00:40
This equals to x squared minus 16x divided by x minus 8 squared.
00:54
Now f prime of x equals to 0, if the numerator of that expression equals to 0, if x squared minus 16, x equals 0, we can rewrite that as x times x minus 16 equals 0.
01:11
That gives us two possibilities.
01:13
Either x equals 0 or x minus 16 equals 0 from which it follows that x must be equal to 16.
01:24
So these are the x coordinates at which the tangent line is horizontal.
01:29
Now let's find the y coordinates.
01:33
For x equals 0, y equals to f of 0...