求下列函式在指定閉區間上的最大值和最小值 (1)F(x7)=2x^3-17x^2+42x-28[1,5] 解析：∵F(x)=2x^3-17x^2+42x-28 令F’(x)=6x^2-34x+42=0==>3x^2-17x+21=0==>x1=(17-√37)/6，x2=(17+√37)/6 F’’(x)=12x-34==>F”(x1)0，∴函式F(x)在x2處取極小值F(x2)≈-4.1493 F(1)=-1，F(5)=7 ∴函式F(x)在區間[1,5]上最大值為F(5)=7，最小值為F(x2)≈-4.1493 (2)G(x)=e^x(x^2-4x+3)[-3,2] 解析：∵G(x)=e^x(x^2-4x+3) 令G’(x)=e^x(x^2-4x+3)+e^x(2x-4)=e^x(x^2-2x-1)=0==>x1=1-√2,x2=1+√2 G’’(x)=e^x(x^2-2x-1)+e^x(x-2)=e^x(x^2-x-3) G’’(x1)0，∴函式G(x)在x2處取極小值G(x2)≈-9.2626 G(-3)=1.1949，G(2)=-7.3891 ∴函式G(x)在區間[-3,2]上最大值為G(x1)=3.1909，最小值為G(2)≈-7.3891