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