Câu hỏi 38

\(\begin{array}{l}f\left( x \right) = 3\left( {{{\sin }^4}x + {{\cos }^4}x} \right) - 2\left( {{{\sin }^6}x + {{\cos }^6}x} \right)\\f\left( x \right) = 3\left[ {{{\left( {{{\sin }^2}x + {{\cos }^2}x} \right)}^2} - 2{{\sin }^2}x{{\cos }^2}x} \right]\\\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, - 2\left[ {{{\left( {{{\sin }^2}x + {{\cos }^2}x} \right)}^3} - 3{{\sin }^2}x{{\cos }^2}x\left( {{{\sin }^2}x + {{\cos }^2}x} \right)} \right]\\f\left( x \right) = 3\left[ {1 - \dfrac{1}{2}{{\sin }^2}2x} \right] - 2\left( {1 - \dfrac{3}{4}{{\sin }^2}2x} \right)\\f\left( x \right) = 3 - \dfrac{3}{2}{\sin ^2}2x - 2 + \dfrac{3}{2}{\sin ^2}2x = 1\\ \Rightarrow f'\left( x \right) = 0\,\,\forall x \in \mathbb{R} \Rightarrow f'\left( {2018} \right) = 0\end{array}\)

Chọn D.