Let I := [0; /2] and let f : I R be defined by f(x) :=

Let I := [0; π/2] and let f : I → R be defined by f(x) := sup{x2, cos x} for x ∈ I. Show there exists an absolute minimum point x0 ∈ I for f on I. Show that x0 is a solution to the equation cos x = x2.