Fermi
·
Concept Library
·
Courses
·
Books
·
Problems
·
Simulations
·
Math Wiki
·
High School
Fermi
›
Problems
Mathematics
Mathematics
Problem
If a function
f
(
x
)
f(x)
f
(
x
)
is differentiable at
x
=
3
x=3
x
=
3
, which one of the following statements must be true? a)
f
′
(
x
)
f'(x)
f
′
(
x
)
is continuous at
x
=
3
x=3
x
=
3
b)
f
(
x
)
f(x)
f
(
x
)
is monotonic in some neighbourhood of
x
=
3
x=3
x
=
3
c)
f
(
x
)
f(x)
f
(
x
)
is continuous at
x
=
3
x=3
x
=
3
d)
lim
h
→
0
f
(
3
+
h
)
−
f
(
3
)
h
\displaystyle \lim_{h\to0}\frac{f(3+h)-f(3)}{h}
h
→
0
lim
h
f
(
3
+
h
)
−
f
(
3
)
is infinite
Browse the problem library