00:01
Well, i have to find the point on this curve here, which is x cubed minus x, where the tangent to this curve passes through the secant line that passes through the point.
00:14
The points, let's see here, minus one, x equals minus one on the curve, and x equals two.
00:22
So here we have x equals minus one is just zero here.
00:30
So that's one point on the second.
00:31
And when x equals 2 we have 8 of 6 so right here so this is the secant line here in green and so we want to find this line here which is tangent has the same slope is parallel um and it's tangent to the curve so you need to take the derivative so the derivative is 3x squared minus 1 the tangent line the tangent line is given by f prime at the point of interest times x minus that point plus the function evaluated that point.
01:05
We can plug this in, and we wind up with this expression here.
01:10
And so we can see this is our slope here, the tangent line, given whatever point that we have.
01:18
And so what we can do is then we can figure out what the slope of this line is here.
01:24
So that slope, we have a span here of three, and so the difference was six...