which of the following are not well behaved funtions:
a)ax^2 + bx+c
b)e^x for all x
c)y= |x|
d)g(x) = cosx + sinx for -pie=< x =< pie and 0 elsewhere
(sigh)
Would you eat $\displaystyle \pi$? No. So don't spell it "pie," spell it correctly: "pi."
Okay, this might be what you need: $\displaystyle y = |x|$ is not "smooth." That is to say all the derivatives of y are not continuous. (In fact no derivative of this function is continuous.) In this sense $\displaystyle y = |x|$ is not well behaved.
-Dan