Let u: r r be a twice continuously differentiable fiunction such that u(0) >>0 and u'(0) >0. suppose u satisfies u(t) u"(x) = 1l2 for all x e r. -x2 consider th

Let u: R R be a twice continuously differentiable fiunction such that u(0) >>0 and u'(0) >0. Suppose u satisfies u(T) u"(x) = 1L2 for all x E R. -x2 Consider the following two statements: I. The function uu' is monotonically increasing on [0, co). IL. The function u is monotonically increasing on [0, co). Then which one of the following is corect? puoABoth I and II are false. B. Iis true, but II is false. c. Iis false, but II is true. D. Both I and II are true.