(a) Show that if a differentiable function f : RN _> R has a local minimum at co E R then all of its first order partial derivatives at this point are zero. (b) f(ac) = ||a|/2 (assume Euclidean norm) is differentiable everywhere, and assumes its minimum and maximum on any compact set, however, its partial derivatives are only zero at the origin. Explain why it does not contradict part(a)