Fermi
·
Concept Library
·
Courses
·
Books
·
Problems
·
Simulations
·
Math Wiki
·
High School
Fermi
›
Problems
Mathematics
Mathematics
Problem
Let
f
(
x
)
=
x
3
−
3
x
2
+
3
k
x
f(x)=x^{3}-3x^{2}+3k x
f
(
x
)
=
x
3
−
3
x
2
+
3
k
x
. The function has two critical points
c
1
c_{1}
c
1
and
c
2
c_{2}
c
2
. Find the range of real values of
k
k
k
for which the local maximum of
f
f
f
occurs at a negative
x
x
x
–value and the local minimum occurs at a positive
x
x
x
–value.
Browse the problem library