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\( \xi \)= ________。______
举一反三
- 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\( f\left( x \right) = 5{x^2} + x - 2 \)在区间\( \left[ {0,1} \right] \)上满足拉格朗日中值定理（ ）
- 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\( f\left( x \right) = 2{x^2} - x - 3 \)在区间\( \left[ { - 1,1.5} \right] \)上满足罗尔定理的点是 ________. ______
- 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: \( {3 \over 7} \)