Fermi
·
Concept Library
·
Courses
·
Books
·
Problems
·
Simulations
·
Math Wiki
·
High School
Fermi
›
Problems
Mathematics
Mathematics
Problem
Let
f
f
f
be continuous on
R
\mathbb R
R
and define
g
g
g
by
g
(
x
)
=
∫
1
x
f
(
t
)
d
t
g(x)=\displaystyle\int_{1}^{x} f(t)\,dt
g
(
x
)
=
∫
1
x
f
(
t
)
d
t
. Which of the following statements must be true for every real number
x
x
x
? a)
g
′
(
x
)
=
∫
1
x
f
′
(
t
)
d
t
g'(x)=\displaystyle\int_{1}^{x} f'(t)\,dt
g
′
(
x
)
=
∫
1
x
f
′
(
t
)
d
t
b)
g
′
(
x
)
=
f
(
x
)
g'(x)=f(x)
g
′
(
x
)
=
f
(
x
)
c)
g
(
x
)
=
f
′
(
x
)
g(x)=f'(x)
g
(
x
)
=
f
′
(
x
)
d)
g
′
(
x
)
=
f
′
(
x
)
g'(x)=f'(x)
g
′
(
x
)
=
f
′
(
x
)
Browse the problem library