已知函数g（x）=a-x3（≤x≤e，e为自然对数的底数）与h（x）=3lnx的图象上存在关于x轴对称的点，则实数a的取值范围是（）A.[1，e3-3]B.[1e3+3，e3-3]C.[1，1e3+3]D.[e3-3，+∞）

Question

已知函数g（x）=a-x³（≤x≤e，e为自然对数的底数）与h（x）=3lnx的图象上存在关于x轴对称的点，则实数a的取值范围是（　　）

A. [1，e³-3]

B. [

(1)/(e3)+3，e3-3]

C. [1，

(1)/(e3)+3]

D. [e³-3，+∞）

Answer 1

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\u8bbef\uff08x\uff09=3lnx-x3\uff0c\u6c42\u5bfc\u5f97\uff1af\u2032\uff08x\uff09=-3x2=\uff0c
\u2235\u2264x\u2264e\uff0c\u2234f\u2032\uff08x\uff09=0\u5728x=1\u6709\u552f\u4e00\u7684\u6781\u503c\u70b9\uff0c
\u2235f\uff08\uff09=-3-\uff0cf\uff08e\uff09=3-e3\uff0cf\uff08x\uff09_{\u6781\u5927\u503c=f\uff081\uff09=-1\uff0c\u4e14\u77e5f\uff08e\uff09<f\uff08\uff09\uff0c
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\u4ece\u800ca\u7684\u53d6\u503c\u8303\u56f4\u4e3a[1\uff0ce3-3]\uff0e
\u6545\u9009\uff1aA\uff0e" "latex":"}}

\u7531\u5df2\u77e5\uff0c\u5f97\u5230\u65b9\u7a0ba-x^{3=-3lnx\u21d4-a=3lnx-x3\u5728[$\\dfrac {1} {e}$\uff0ce]\u4e0a\u6709\u89e3\uff0e
\u8bbef\uff08x\uff09=3lnx-x3\uff0c\u6c42\u5bfc\u5f97\uff1af\u2032\uff08x\uff09=$\\dfrac {3} {x}$-3x2=$\\dfrac {3(1-{x}^{3})} {x}$\uff0c
\u2235$\\dfrac {1} {e}$\u2264x\u2264e\uff0c\u2234f\u2032\uff08x\uff09=0\u5728x=1\u6709\u552f\u4e00\u7684\u6781\u503c\u70b9\uff0c
\u2235f\uff08$\\dfrac {1} {e}$\uff09=-3-$\\dfrac {1} {{e}^{3}}$\uff0cf\uff08e\uff09=3-e3\uff0cf\uff08x\uff09_{\u6781\u5927\u503c=f\uff081\uff09=-1\uff0c\u4e14\u77e5f\uff08e\uff09<f\uff08$\\dfrac {1} {e}$\uff09\uff0c
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\u4ece\u800ca\u7684\u53d6\u503c\u8303\u56f4\u4e3a[1\uff0ce3-3]\uff0e
\u6545\u9009\uff1aA\uff0e"}}}