Fermi
·
Concept Library
·
Courses
·
Books
·
Problems
·
Simulations
·
Math Wiki
·
High School
Fermi
›
Problems
Mathematics
Mathematics
Problem
For a real parameter
k
k
k
, define
f
k
(
x
)
=
x
3
−
2
k
x
+
k
f_k(x)=x^{3}-2kx+k
f
k
(
x
)
=
x
3
−
2
k
x
+
k
on the interval
[
0
,
2
]
[0,2]
[
0
,
2
]
. For which values of
k
k
k
is at least one real solution of
f
k
(
x
)
=
0
f_k(x)=0
f
k
(
x
)
=
0
guaranteed to occur in
(
0
,
2
)
(0,2)
(
0
,
2
)
? a)
0
<
k
<
8
3
0<k<\dfrac{8}{3}
0
<
k
<
3
8
b) All\ real\ k c)
k
<
0
or
k
>
8
3
k<0\text{ or }k>\dfrac{8}{3}
k
<
0
or
k
>
3
8
d)
k
≤
0
or
k
≥
8
3
k\le 0\text{ or }k\ge \dfrac{8}{3}
k
≤
0
or
k
≥
3
8
Browse the problem library