3. D. If f(x) is continuously derivable, then f' (x0) = 0; If f(x) is continuous but non-differentiable, then f'(x0) does not exist, such as f(x)=-|x|, and there is a maximum at x=0.

4, C .Y=xlnx, then y' = lnx+ 1.y'' = 1/x, y'' =-1/x 2.

5. C. This is a piecewise function. For different ranges of X, the corresponding expressions are different. When calculating the function value of the factor, we must first judge the interval where X is located.