Fermi
·
Concept Library
·
Courses
·
Books
·
Problems
·
Simulations
·
Math Wiki
·
High School
Fermi
›
Problems
Problem
Problem
If
f
′
(
1
)
=
1
f'(1) = 1
f
′
(
1
)
=
1
and
d
d
x
(
f
(
2
x
)
)
=
f
′
(
x
)
\frac{d}{dx}(f(2x)) = f'(x)
d
x
d
(
f
(
2
x
))
=
f
′
(
x
)
,
∀
x
>
0
\forall x > 0
∀
x
>
0
. If
f
′
(
x
)
f'(x)
f
′
(
x
)
is differentiable, then there exists a number
c
∈
(
2
,
4
)
c \in (2, 4)
c
∈
(
2
,
4
)
such that
f
′
′
(
c
)
f''(c)
f
′′
(
c
)
is equal to a.
−
1
/
4
-1/4
−
1/4
b.
−
1
/
8
-1/8
−
1/8
c.
1
/
4
1/4
1/4
d.
1
/
8
1/8
1/8
Browse the problem library