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。（ ）
举一反三
- 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\( \xi \)= ________。______
- 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\( f\left( x \right) = 2{x^2} - x - 3 \)在区间\( \left[ { - 1,1.5} \right] \)上满足罗尔定理的点是 ________. ______
- 函数\( f\left( x \right) = x\sqrt {3 - x} \)在区间\( \left[ {0,3} \right] \)上满足罗尔定理的数值\( \xi \)= ______ .
- 若\({y_1}\left( x \right), {y_2}\left( x \right)\)都是\(y' + P\left( x \right)y = Q\left( x \right)\)的特解，且 \({y_1}\left( x \right), {y_2}\left( x \right)\) 线性无关，则通解可表为\(y\left( x \right) = {y_1}\left( x \right) + C\left[ { { y_1}\left( x \right) - {y_2}\left( x \right)} \right]\)。