Solving Piecewise Functions in C_p (0, pi) and C ' _p (0, pi)

[jaejoon89]

Homework Statement

Which are in C_p (0, pi) and/or in C ' _p (0, pi)?

f(x) = {x if 0 < x < pi/2, pi-x if pi/2 < x < pi
g(x) = {sqrt(x) if 0 < x < pi/3, (pi-x)^2 if pi/3 < x < pi
h(x) = {x if 0 < x < pi/2, ln(pi-x) if pi/2 < x < pi

Homework Equations

(see equations above)

The Attempt at a Solution

I know C_p means "piecewise continuous" but what is C ' _p? How do you do these? I've been racking my brain on this, am completely lost.

 

[Dick]

If you know what piecewise continuous is, that's good. Which are? I have no clue what C'_p means. Can you look it up and tell us?

 

[jaejoon89]

I looked in my book and lecture notes - they don't say!

 

[Dick]

Then you have perfect justification for not answering the question. Seek clarification. Do you think it might mean differentiable?

 

[Mark44]

Or maybe piecewise differentiable

 

[HallsofIvy]

That would be my guess.