x4次方×（1－x²）最小值

x4次方×（1－x²）最小值
x4次方×（1－x²）最小值

x4次方×（1－x²）最小值
X^2(1-X^2)
=4 (1/2X^2)(1/2X^2)(1-X^2)
≤4×［(1/2X^2+1/2X^2+1-X^2)/3］^3
=4×1/27
=4/27,
∴当且仅当1/2X^2=1-X^2,
X^2=2/3
X=±√6/3时,
原式最小=4/27.

X^4(1-X^2)
=4 (1/2X^2)(1/2X^2)(1-X^2)
≤4×［(1/2X^2+1/2X^2+1-X^2)/3］^3
=4×1/27
=4/27，
∴当且仅当1/2X^2=1-X^2，
X^2=2/3
X=±√6/3时，
原式最小=4/27。