. Find all critical points and then use the rst-derivative test to determine local maxima and minima for f(x) = x + l/x Show that if a is a positive constant, then x = 0 is the only critical point of f (x) = x + OJ; . Use derivatives to show that f is increasing and its graph is concave down for all x > 0 . Find the global maximum and minimum for the function f(x) = x4 8x2 on the closed interval [-3, l] . Find all extrema and inection points, and apply the second derivative test to nd the relative minimum and maximum of the function f(x) = x3 3x2 - 24x + 32. Also discuss the concavity of the graph. . For positive constants A and B, the force between two atoms in a molecule is given by f (r) = g + A; where r > 0 is the distance between the atoms. What value of r r r minimizes the force between the atoms