Cho hàm số \(f\left( x \right) = \sqrt {x + 3} \). Giá trị của \(x.f\left( 1 \right) - \left( {x - 1} \right).

* Hướng dẫn giải

\(\begin{array}{l}
f\left( 1 \right) = 1,f'\left( x \right) = \frac{1}{{2\sqrt {x + 3} }} \Rightarrow f'\left( 1 \right) = \frac{1}{4}\\
f''\left( x \right) = \frac{{ - \left( {\sqrt {x + 3} } \right)'}}{{2\left( {x + 3} \right)}} = \frac{{ - 1}}{{4\left( {x + 3} \right)\sqrt {x + 3} }} \Rightarrow f''\left( 1 \right) =  - \frac{1}{{32}}\\
 \Rightarrow x.f\left( 1 \right) - \left( {x - 1} \right)f'\left( 1 \right) - 16f''\left( 1 \right) = 2x - \frac{{x - 1}}{4} + \frac{1}{2} = \frac{{7x3}}{4}
\end{array}\)