00:01
A tangent line is a line that intersects a curve locally at one point.
00:07
Another way to think about this is imagine i zoom in sufficiently to the graph at 2 .5.
00:12
So i could just keep zooming into that point.
00:16
And eventually, what i see is almost a line.
00:19
So the more i zoom in, the less sort of nuanced nature of the curve that i see and more of what appears to be a line.
00:26
That's the tangent line.
00:28
So if we want to draw the tangent line at 2 .5, if i imagine extending this graph at that moment just to be a line, it would look something like this.
00:40
So now we want to estimate the slope of that tangeline.
00:45
So let's see what that slope would be...