函数y=8x2-lnx的单调减区间是______,极小值是______.
因为y=f(x)=8x2-lnx,
∴f'(x)=16x-
=1 x
=16x2-1 x 16(x-
)(x+1 4
)1 4 x
∵x>0
∴当x>
时,f'(x)>0,即f(x)递增;1 4
当0<x<
时,f'(x)<0,f(x)递减.1 4
且f(x) 极小值为f(
)=8×(1 4
)2-ln1 4
=1 4
+2ln2.1 2
故答案为:(0,
),1 4
+2ln2.1 2
函数y=8x2-lnx的单调减区间是______,极小值是______.
因为y=f(x)=8x2-lnx,
∴f'(x)=16x-
=1 x
=16x2-1 x 16(x-
)(x+1 4
)1 4 x
∵x>0
∴当x>
时,f'(x)>0,即f(x)递增;1 4
当0<x<
时,f'(x)<0,f(x)递减.1 4
且f(x) 极小值为f(
)=8×(1 4
)2-ln1 4
=1 4
+2ln2.1 2
故答案为:(0,
),1 4
+2ln2.1 2