Question

求函数f(x)=(x+1)(x+2)(x+3)(x+4)+15的最小值

Answer 1

f(x)=(x+1)(x+2)(x+3)(x+4)+15=（x+1)(x+4)(x+2)(x+3)+15

=(x^2+5x+4)(x^2+5x+6)+15

=(x^2+5x)^2+10(x^2+5x)+39

=(x^2+5x+5)^2+14

>=14

x=-2.5时等号成立

最小值为14