求函数在指定的闭区间的最大值和最小值G(x)=e×(x²-4x+3),[-3,2].

G'(x)=e^x(x^2-4x+3+2x-4)=e^x(x^2-2x-1)由G'(x)=0,得x^2-2x-1=0得极值点x=1+√2,1-√2在[-3,2]G(1-√2)=e^(1-√2)(3-2√2-4+4√2+3)=e^(1-√2)(2+2√2)为极大值端点值：G(-3)=e^(-3)(9+12+3)=24e^(-3)G(2)=e^2(4-8+3)=-e^2比较得：最小值为G(2)=-e^2最大值为G(1-√2)=e^(1-√2)(2+2√2)