Câu hỏi 16

Xét khoảng \(\left( {0;\,3} \right)\) ta có: \(\left\{ \begin{array}{l}F\left( x \right) = {x^2} - 4x + 7\\G\left( x \right) = \dfrac{1}{2}x + 1\end{array} \right. \Rightarrow \left\{ \begin{array}{l}F'\left( x \right) = 2x - 4\\G'\left( x \right) = \dfrac{1}{2}\end{array} \right.\)

Ta có: \(P\left( x \right) = F\left( x \right).G\left( x \right)\)

\(\begin{array}{l} \Rightarrow P'\left( x \right) = F'\left( x \right).G\left( x \right) + F\left( x \right).G'\left( x \right)\\ \Rightarrow P'\left( 2 \right) = F'\left( 2 \right).G\left( 2 \right) + F\left( 2 \right).G'\left( 2 \right)\\ = \left( {2.2 - 4} \right).2 + 3.\dfrac{1}{2} = \dfrac{3}{2}.\end{array}\)

Chọn C.