Thread: Chain Rule Question

This one comes in two parts, but is basically the same question:

a) If , find and sketch the graphs of and . Where is not differentiable?

b) a) If , find and sketch the graphs of and . Where is not differentiable?

So, I believe that and , and know how to graph each of these functions. What I am not confident on is the part about where are these functions not differentiable? As I look at the graphs, it looks to me like they are both differentiable across all real numbers. Am I missing something?

They are not differentiable across all real numbers becasue they have sharp corner curves or 'cusps'.

For the first function these appear at the zeros of

Do you follow?

I follow the rule of not being differentiable at sharp corners. Maybe my graph is too small to tell, but I didn't realize that there were sharp corners at the zeros of

Thanks for your help. I appreciate it.