Question

将8分为两数之和,使其立方之和为最小,则分法为(    )

A.2和6                              B.4和4

C.3和5                              D.以上都不对

Answer 1

思路解析:设一个数为x,则另一个数为8-x,则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.

当0≤x＜4时,y′＜0;当4＜x≤8时,y′＞0.所以x=4时,y最小.

答案:B