91Ó°ÊÓ

Find subdifferentials of the following functions: (a) \(f(x)=a|x|, a>0\) (b) \(f(x)=|x-1|+|x+1|\).

Let \(f\) be twice differentiable on an open interval \(I\). Suppose that there exist \(a, b, c \in I\) with \(af(c)\). Prove that there exists \(d \in(a, c)\) such that \(f^{\prime \prime}(d)<0\)