函数\( f\left( x \right) = {x^3} \)在区间\( \left[ {1,2} \right] \)上满足拉格朗日中值定理的数值\( \xi \)=（ ）.
A: \( { { \sqrt {21} } \over 3} \)
B: \( { { \sqrt {21} } \over 7} \)
C: \( {7 \over 3} \)
D: \( {3 \over 7} \)
A: \( { { \sqrt {21} } \over 3} \)
B: \( { { \sqrt {21} } \over 7} \)
C: \( {7 \over 3} \)
D: \( {3 \over 7} \)
举一反三
- 求函数$y = \root 3 \of {x + \sqrt x } $的导数$y' = $( ) A: ${{1 + 2\sqrt x } \over {\root 3 \of {{{\left( {x + \sqrt x } \right)}^2}} }}$ B: $ {{1 + 2\sqrt x } \over {6\root 3 \of {{{\left( {x + \sqrt x } \right)}^2}} }}$ C: $ {{1 + 2\sqrt x } \over {6\sqrt x \cdot \root 3 \of {{{\left( {x + \sqrt x } \right)}^2}} }}$ D: $ {{1 + 2\sqrt x } \over {\sqrt x \cdot \root 3 \of {{{\left( {x + \sqrt x } \right)}^2}} }}$
- 函数\( f\left( x \right) = x\sqrt {3 - x} \)在区间\( \left[ {0,3} \right] \)上满足罗尔定理的数值\( \xi \)= ______ .
- 函数\( f\left( x \right) = {x^3} \)与\( g\left( x \right) = {x^2} + 1 \)在区间\( \left[ {1,2} \right] \)上不满足柯西中值定理。（ ）
- 函数\( f\left( x \right) = {x^2} \)在区间\( \left[ {1,2} \right] \)上满足拉格朗日中值定理的数值\( \xi \)= ________。______
- 设\( {\alpha _1} = {\left( {1,2, - a, - 3} \right)^T},{\alpha _2} = {\left( { - 3,2,4,1} \right)^T} \)且\( \left( { { \alpha _1},{\alpha _2}} \right) = - 1 \)，则\( a = \)（ ） A: \( - {2 \over 3} \) B: \( - {3 \over 4} \) C: \( - {1 \over 4} \) D: \( {1 \over 2} \)