Fermi
·
Concept Library
·
Courses
·
Books
·
Problems
·
Simulations
·
Math Wiki
·
High School
Fermi
›
Problems
Mathematics
Mathematics
Problem
A differentiable function
f
f
f
satisfies
f
(
0
)
=
2
f(0)=2
f
(
0
)
=
2
with
f
′
(
0
)
=
0
f'(0)=0
f
′
(
0
)
=
0
and
f
(
−
1
)
=
0
f(-1)=0
f
(
−
1
)
=
0
where the tangent to the graph is vertical (so
f
′
f'
f
′
is undefined at
x
=
−
1
x=-1
x
=
−
1
). For
g
=
f
−
1
g=f^{-1}
g
=
f
−
1
, determine (a)
g
′
(
2
)
g'(2)
g
′
(
2
)
(b) whether
g
′
(
0
)
g'(0)
g
′
(
0
)
exists, and if so, its value.
Browse the problem library