Determine if the graph of the function f ( x ) f\left(x\right) f ( x ) is continuous and/or differentiable at x = 1 x=1 x = 1 .

give this problem a try. So here we're asked to determine if the graph of the function f of x is continuous and or differentiable at x equals 1. Okay. Now to solve this problem, I'm first going to figure out whether or not this graph is continuous. So the way that I can do this is by tracing this graph with my pen. Now as I can see, as I trace this graph, I can draw this all in one stroke. I don't have to pick up my pen at any point. So because of this, we would see that this graph is continuous. Now is the graph differentiable? Well, being continuous is one of the criteria for the graph being differentiable, but there's another criteria we have to meet also. We cannot have any sharp corners or turns for a graph to be differentiable at a point. Now looking at this point x equals 1, it appears that there clearly is a sharp corner right there. There's a corner or return that happens sharply, and because of that, that means the graph is not going to be differentiable. So we could see that this function is continuous, but not differentiable, and that would be the solution. So hope you found this video helpful.