y ′ ( π/ 3 ) = 2 .

a) Ta có \(y' = 4\cos 2x + \sin \left( {x - \frac{\pi }{3}} \right)\). Khi đó \(y'\left( {\frac{\pi }{3}} \right) = 4\cos \frac{{2\pi }}{3} + \sin \left( {\frac{\pi }{3} - \frac{\pi }{3}} \right) = - 2\).

b) \(y'' = - 8\sin 2x + \cos \left( {x - \frac{\pi }{3}} \right)\).

c) \(y''\left( 0 \right) = - 8\sin 0 + \cos \left( {0 - \frac{\pi }{3}} \right) = \frac{1}{2}\).

d) \(y'\left( {\frac{\pi }{3}} \right) - 2y''\left( 0 \right) = - 2 - 2.\frac{1}{2} = - 3\).

Đáp án: a) Sai;   b) Đúng;   c) Sai;   d) Sai.