1. Which of the above functions are not continuous where they are defined? Why?

Question

2. Which of the above functions are not differentiable where they are defined? Why?

Photo Link: goo.gl/photos/2RPU1dAWoKzUn4Pf8

For the first question, I said that graph F is not continuous because of a jump, but I'm missing another one from those 6 graphs.

For the second question, I said b is not differentiable because of corners, but I appear to be missing 3 more. I initially answered C, D, and F but those aren't correct.

(All 6 graphs are part of the questions and A and a are two different graphs fyi)

Any help is greatly appreciated!

Answer 1

For continuous, ya got me. Only F looks like it fails.

For differentiable, surely F fails, because it isn't even continuous. Also, (a),(b),(d) fail because of the cusps. I am assuming that d(0) is defined somewhere on the y-axis.

(f) fails because the ends of the semi-circle have vertical tangents.