一、选择题
题目1：已知函数\(f(x)=ax^2+bx+c\)，其中\(a\neq 0\)，若\(f(1)=2\)，\(f(2)=5\)，\(f(3)=10\)，则\(a+b+c=\)
解析：
由题意得：
$\(
\begin{cases}
a+b+c=2 \\
4a+2b+c=5 \\
9a+3b+c=10
\end{cases}
\)$
将第一个方程乘以2，得到：
$\(
\begin{cases}
2a+2b+2c=4 \\
4a+2b+c=5 \\
9a+3b+c=10
\end{cases}
\)$
将第一个方程从第二个方程中减去，得到：
$\(
\begin{cases}
2a+2b+2c=4 \\
2a+b=1 \\
9a+3b+c=10
\end{cases}
\)$
将第一个方程从第三个方程中减去，得到：
$\(
\begin{cases}
2a+2b+2c=4 \\
2a+b=1 \\
6a+2b=6
\end{cases}
\)$
将第二个方程乘以2，得到：
$\(
\begin{cases}
2a+2b+2c=4 \\
4a+2b=2 \\
6a+2b=6
\end{cases}
\)$
将第二个方程从第三个方程中减去，得到：
$\(
\begin{cases}
2a+2b+2c=4 \\
4a+2b=2 \\
2a=4
\end{cases}
\)$
解得：\(a=2\)，\(b=-3\)，\(c=1\)。
因此，\(a+b+c=2-3+1=0\)。
答案：0
题目2：设\(a>0\)，\(b>0\)，\(c>0\)，若\(a+b+c=3\)，则\(\sqrt{a}+\sqrt{b}+\sqrt{c}\)的最大值为
解析：
由柯西不等式得：
$\(
(a+b+c)(\sqrt{a}+\sqrt{b}+\sqrt{c})^2 \geq (a+b+c)^2
\)$
即：
$\(
3(\sqrt{a}+\sqrt{b}+\sqrt{c})^2 \geq 9
\)$
解得：
$\(
\sqrt{a}+\sqrt{b}+\sqrt{c} \leq 3
\)$
当且仅当\(a=b=c=1\)时，等号成立。
答案：3
二、填空题
题目1：已知函数\(f(x)=x^3-3x^2+4x-1\)，则$f’(1)=______________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________
