00:01
We're given this graph and we're asked to find the points where the function is not continuous and the points where the function is not differentiable.
00:08
So let's start with evaluating the continuity.
00:14
Now if we just look at this graph, it's very smooth.
00:18
There are no jumps, there are no gaps, there are no vertical asymptotes, every point is defined, and every point is continuous.
00:28
So there are no points on this graph where the function is not.
00:32
Continuous.
00:38
Let's go ahead and look at the differentiability.
00:42
Now there are no points where this function is not continuous, so we'll be looking for points where there is a vertical tangent, a corner, or a cusp.
00:52
Because we know those points are not differentiable.
00:55
So let's start at the left.
00:57
One looks fine.
00:59
At two here we have a vertical tangent line and functions are not differentiable at vertical tangent lines...