Fermi
·
Concept Library
·
Courses
·
Books
·
Problems
·
Simulations
·
Math Wiki
·
High School
Fermi
›
Problems
Problem
Problem
If
m
m
m
and
n
n
n
are positive integers and
f
(
x
)
=
∫
1
x
(
t
−
a
)
2
n
(
t
−
b
)
2
m
+
1
d
t
f(x) = \int_{1}^{x} (t-a)^{2n} (t-b)^{2m+1} dt
f
(
x
)
=
∫
1
x
(
t
−
a
)
2
n
(
t
−
b
)
2
m
+
1
d
t
,
a
≠
b
a \ne b
a
=
b
, then a.
x
=
b
x = b
x
=
b
is a point of local minimum b.
x
=
b
x = b
x
=
b
is a point of local maximum c.
x
=
a
x = a
x
=
a
is a point of local minimum d.
x
=
a
x = a
x
=
a
is a point of local maximum
Browse the problem library