Question

已知函数f(x)=x^2+2ax+2,x∈[-5,5],求函数在区间[-5,5]上的最小值g(a).

Answer 1

f(x)=x^2+2ax+a^2+2-a^2,对称轴为x=-a
-5<=a<=5时，f(x)最小值为2-a^2,g(a)=2-a^2;
a<-5时,f(x)最小值为x=5时，g(a)=27+10a;
a>5时,f(x)最小值为x=-5时，g(a)=27-10a.

Answer 2

a>5时 -a<-5 f(-5)最小为27-10a
a<-5时 -a>5 f(5)最小为27+10a
-5≤a≤5时 f(-a)最小为2-a^2
g(a)=27-10a a>5
27+10a a<-5
2-a^2 -5≤a≤5