00:01
So this question, we want to find tangent, find all points.
00:09
So find all points at which a tangent line is horizontal on the graph of a function.
00:30
And we're not actually given the function, so we'll just have to explain how to do this for a general function.
00:36
So what we have is if we have some function, and we're thinking about where is the tangent line horizontal, well, the tangent line goes off parallel to the curve at any given point.
00:52
So where it's horizontal are going to be the points where the derivative of that curve is zero.
00:58
So we get a horizontal tangent.
01:04
This is going to be at a point where the derivative is zero.
01:07
So f dash of x equals zero here.
01:12
So what we do is if we say that we have some curve y equals f of x, then the tangent, y tangent at a point x, let's say x0 as a function of x, is going to be f of x0 plus x minus x0 times f dash of x0.
01:43
And this is just a first order tailor expansion...