Fermi
·
Concept Library
·
Courses
·
Books
·
Problems
·
Simulations
·
Math Wiki
·
High School
Fermi
›
Problems
Mathematics
Mathematics
Problem
Let
f
f
f
be a differentiable function on
R
\mathbb{R}
R
such that
f
(
2
)
=
1
f(2) = 1
f
(
2
)
=
1
,
f
′
(
2
)
=
4
f'(2) = 4
f
′
(
2
)
=
4
. Let
lim
x
→
0
(
f
(
2
+
x
)
)
3
/
x
=
e
α
\lim_{x \to 0} (f(2+x))^{3/x} = e^\alpha
lim
x
→
0
(
f
(
2
+
x
)
)
3/
x
=
e
α
. Then the number of times the curve
y
=
4
x
3
−
4
x
2
−
4
(
α
−
7
)
x
−
α
y = 4x^3 - 4x^2 - 4(\alpha - 7)x - \alpha
y
=
4
x
3
−
4
x
2
−
4
(
α
−
7
)
x
−
α
meets
x
x
x
-axis is :-
Browse the problem library