Đáp án:
\( f\left( { - 2} \right) = 24.\)
Giải thích các bước giải:
\(\begin{array}{l}
y = f\left( x \right) = {x^3} + a{x^2} + bx + c\\
\Rightarrow y' = 3{x^2} + 2ax + b\\
\Rightarrow y' = 0 \Leftrightarrow 3{x^2} + 2ax + b = 0\\
Hs\,\,dat\,\,cuc\,\,tri\,\,tai\,\,x = 1\\
\Rightarrow y'\left( 1 \right) = 0 \Leftrightarrow 3 + 2a + b = 0\\
\Leftrightarrow 2a + b = - 3\,\,\,\,\left( 1 \right)\\
f\left( 3 \right) = 29 \Leftrightarrow 27 + 9a + 3b + c = 29\\
\Leftrightarrow 9a + 3b + c = 2\,\,\,\,\,\left( 2 \right)\\
Dt\,hs\,\,\,cat\,\,Oy\,\,tai\,\,diem\,\,co\,\,tung\,\,do\,\, = 2\\
\Rightarrow c = 2\\
\Rightarrow \left( 2 \right) \Leftrightarrow 9a + 3b = 0\\
\Rightarrow \left\{ \begin{array}{l}
2a + b = - 3\\
9a + 3b = 0
\end{array} \right. \Leftrightarrow \left\{ \begin{array}{l}
a = 3\\
b = - 9
\end{array} \right.\\
\Rightarrow f\left( x \right) = {x^3} + 3{x^2} - 9x + 2\\
\Rightarrow f\left( { - 2} \right) = 24.
\end{array}\)
