Cho y = F (x) và y

C

- Hướng dẫn giải

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

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

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