00:01
To draw a tangent line, we need to consider what does the curve look like at that instant if we zoom in enough.
00:09
So at this point, if i zoom into the curve and continue zooming, imagine i just keep doing that in making the graph look more and more and more like a line.
00:20
So at that moment, i'm going to estimate the tangent line to roughly look like this.
00:28
And it makes sense the tangent line has some positive slope because at that moment the graph is increasing.
00:33
So now we just need to identify two points that we can easily detect that are on this line that aren't necessarily the point of tangency.
00:45
So in looking at the graph, one point that we can estimate is roughly at 3 .7.
00:53
And note, this is not necessarily on the actual function as much as the tangent line.
00:58
And another point that i'm going to estimate is roughly around 2 .5...