已知函数f(x)=2x^3+ax与g(x)=bx^2+c
2个回答
展开全部
f(x)
=
2x^3
+
ax,
f'(x)
=
6x^2
+
a
g(x)
=
bx^2
+
c,
g'(x)
=
2bx
16
+
2a
=
0,
4b
+
c
=
0,
24
+
a
=
4b.
a
=
-8,
b
=
6
+
a/4
=
4,
c
=
-4b
=
-16.
F(x)
=
2x^3
+
ax
+
bx^2
+
c
=
2x^3
+
4x^2
-
8x
-
16,
F'(x)
=
6x^2
+
8x
-
8
=
2[3x^2
+
4x
-
4]
=
2(3x
-
2)(x
+
2)
x
<
-2
时,F'(x)>0.
F(x)单调递增
-2
<
x
<
2/3时,F'(x)
<
0.
F(x)单调递减
x
>
2/3时,F'(x)>0.
F(x)单调递增
=
2x^3
+
ax,
f'(x)
=
6x^2
+
a
g(x)
=
bx^2
+
c,
g'(x)
=
2bx
16
+
2a
=
0,
4b
+
c
=
0,
24
+
a
=
4b.
a
=
-8,
b
=
6
+
a/4
=
4,
c
=
-4b
=
-16.
F(x)
=
2x^3
+
ax
+
bx^2
+
c
=
2x^3
+
4x^2
-
8x
-
16,
F'(x)
=
6x^2
+
8x
-
8
=
2[3x^2
+
4x
-
4]
=
2(3x
-
2)(x
+
2)
x
<
-2
时,F'(x)>0.
F(x)单调递增
-2
<
x
<
2/3时,F'(x)
<
0.
F(x)单调递减
x
>
2/3时,F'(x)>0.
F(x)单调递增
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