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$(1,-10)$为拐点,代入:$y''\vert_{x=1}=6a+2b=0$,$y\vert_{x=1}=a+b+c+d=- 其中$F(x)$满足罗尔定理三个条件:连续、可导、两端点相等。 -\subsubsection{个数} +\subsubsection{已知函数个数} 往往需要多个方法一起确定具体个数。 @@ -731,10 +732,14 @@ $\therefore f'(x)$无实根,所以$t=x^2$解不出来,所以$f'(x)\neq0$。 $f'(x)=0$至多0个根。所以根据罗尔原话$f(x)=0$至多一个根,又由上面至少一个根,所以只有一个根,选择$B$。 +\subsubsection{含参函数个数} + \paragraph{函数含参导数不含参} \leavevmode \medskip 参数是一个加在式子上的常数,函数求导后参数就被消掉了,所以可以在计算过程中不考虑参数,等到了最后的结果再讨论参数。 +当存在参数时要尽可能将参数在导数中消掉,如$e^x=kx$,$f(x)$不能是$e^x-kx$而应该是$\dfrac{e^x}{x}-k$。 + \textbf{例题:}设常数$k>0$,函数$f(x)=\ln x-\dfrac{x}{e}+k$在$(0,+\infty)$内的零点个数为()。 $A.3$\qquad$B.2$\qquad$C.1$\qquad$D.0$