Question

问代数式－x²-3x+2有最大值还是有最小值,并求出当x为何值时,取得最值

Answer 1

－x²-3x+2

=-（x²+3x-2)

=-(x²+3x +9/4 -9/4 - 2)

=-[(x +3/2)²- 17/4]

=-(x +3/2)²+ 17/4

因为(x +3/2)²≥0,当x=-3/2时,取0

所以-(x +3/2)²≤0

所以

-(x +3/2)²+ 17/4≤17/4,当x=-3/2时,取最大值17/4