Question

將8分為兩數(shù)之和,使其立方之和為最小,則分法為(    )

A.2和6                              B.4和4

C.3和5                              D.以上都不對(duì)

Answer 1

思路解析:設(shè)一個(gè)數(shù)為x,則另一個(gè)數(shù)為8-x,則y=x³+(8-x)³,0≤x≤8,

y′=3x²-3(8-x)²,令y′=0,即3x²-3(8-x)²=0,解得x=4.

當(dāng)0≤x＜4時(shí),y′＜0;當(dāng)4＜x≤8時(shí),y′＞0.所以x=4時(shí),y最小.

答案:B