]give a proof by contradiction: let g be any directed graph in which every pair of nodes u and v has exactly one edge (either uv or u v but not both), and let w be a node with highest out-degree. then every node is reachable from w by a path of length 3 2.

For positive constants a and b, the force between two atoms in a molecule is given f(r) = −a r2 + b r3 , where r > 0 is the distance between the atoms. note: a and b are upper case letters. (a) find f '(r) = (b) find the critical point for f(r). r = (c) find f ''(r) = (d) find the value of r so that f ''(r) = 0.