Exercise 7.1. Consider the problem of maximizing (7.1) subject to (7.2) and (7.3) as in Section 7.1. Suppose that for the pair (ˆx (t), yˆ(t)) there exists a time interval (t0 , t00) with t0 < t00 such that λ˙ (t) 6= − [fx (t, xˆ (t), yˆ(t)) + λ (t) gx (t, xˆ (t), yˆ(t))] for all t ∈ ¡ t 0 , t00¢ . Prove that the pair (ˆx (t), yˆ(t)) could not attain the optimal value of (7.1).