$f命题：$设$fleft( x ight) in Cleft[ {a,b} ight]$，则存在$xi in left[ {a,b} ight]$，使得$fleft( xi ight) = frac{{{c_1}fleft( {{x_1}} ight) + cdots + {c_n}fleft( {{x_n}} ight)}}{{{c_1} + cdots + {c_n}}}$，其中${c_i} > 0,a < {x_1} < ... < {x_n} < b$
$f命题：$设$fleft( x ight) in Cleft( {a,b} ight)$，且$lim limits_{x o egin{array}{*{20}{c}}{{a^ + }}end{array}} fleft( x ight) = A,lim limits_{x o egin{array}{*{20}{c}}{{b^ - }}end{array}} fleft( x ight) = B$，则对任意$c in left( {A,B} ight)$，存在$xi in left( {a,b} ight)$，使得$fleft( xi ight) = c $
$f命题：$设$fleft( x ight)$在$left[ {0, + infty } ight)$上有连续导数，且$f'left( x ight) ge k > 0,fleft( 0 ight) < 0$，则$fleft( x ight)$在$left( {0, + infty } ight)$上有且仅有一个零点
$f命题：$开普勒$fleft( {Kepler} ight)$方程$x = varepsilon sin x + aleft( {0 < varepsilon < 1} ight)$只有唯一实根
$f命题：$设$f(x)$在$(a,b)$内二阶可导，$c$为$(a,b)$内一点，满足$f''left( c ight) e 0$，则存在不同的点${x_1},{x_2} in left( {a,b} ight)$，使得[frac{{fleft( {{x_2}} ight) - fleft( {{x_1}} ight)}}{{{x_2} - {x_1}}} = f'left( c ight)]
$f命题：$