已知函數(shù)f(x)=x3-alnx(a∈R).
(1)當(dāng)a=1時(shí),求函數(shù)f(x)極值;
(2)若函數(shù)g(x)=f(x)-32x2在(0,+∞)上遞增,求實(shí)數(shù)a的取值范圍;
(3)函數(shù)f(x)在區(qū)間(1,e]上存在兩個(gè)不同零點(diǎn),求實(shí)數(shù)a的取值范圍.
g
(
x
)
=
f
(
x
)
-
3
2
x
2
【答案】(1),f(x)無極大值;
(2)實(shí)數(shù)a的取值范圍為;
(3)實(shí)數(shù)a的取值范圍為(3e,e3].
f
(
x
)
極小值
=
f
(
1
3
3
)
=
1
+
ln
3
3
(2)實(shí)數(shù)a的取值范圍為
(
-
∞
,-
4
9
]
(3)實(shí)數(shù)a的取值范圍為(3e,e3].
【解答】
【點(diǎn)評(píng)】
聲明:本試題解析著作權(quán)屬菁優(yōu)網(wǎng)所有,未經(jīng)書面同意,不得復(fù)制發(fā)布。
發(fā)布:2024/5/20 8:0:9組卷:19引用:1難度:0.5
相似題
-
1.已知函數(shù)f(x)=x3-2kx2+x-3在R上不單調(diào),則k的取值范圍是 ;
發(fā)布:2024/12/29 13:0:1組卷:236引用:3難度:0.8 -
2.在R上可導(dǎo)的函數(shù)f(x)的圖象如圖示,f′(x)為函數(shù)f(x)的導(dǎo)數(shù),則關(guān)于x的不等式x?f′(x)<0的解集為( ?。?/h2>
發(fā)布:2024/12/29 13:0:1組卷:265引用:7難度:0.9 -
3.已知函數(shù)f(x)=ax2+x-xlnx(a∈R)
(Ⅰ)若函數(shù)f(x)在(0,+∞)上單調(diào)遞增,求實(shí)數(shù)a的取值范圍;
(Ⅱ)若函數(shù)f(x)有兩個(gè)極值點(diǎn)x1,x2(x1≠x2),證明:.x1?x2>e2發(fā)布:2024/12/29 13:30:1組卷:141引用:2難度:0.2