Fermi
·
Concept Library
·
Courses
·
Books
·
Problems
·
Simulations
·
Math Wiki
·
High School
Fermi
›
Problems
Mathematics
Mathematics
Problem
Consider the function
f
(
x
)
=
x
3
−
5
x
+
4
f(x)=x^{3}-5x+4
f
(
x
)
=
x
3
−
5
x
+
4
. For
c
>
1
c>1
c
>
1
, the average rate of change of
f
f
f
on the interval
[
1
,
c
]
[1,c]
[
1
,
c
]
equals the instantaneous rate of change of
f
f
f
at
x
=
2
x=2
x
=
2
. What is the value of
c
c
c
? a)
2
2
2
b)
−
1
+
3
5
2
\dfrac{-1+3\sqrt5}{2}
2
−
1
+
3
5
c)
1
+
3
5
2
\dfrac{1+3\sqrt5}{2}
2
1
+
3
5
d)
−
1
+
45
3
\dfrac{-1+\sqrt{45}}{3}
3
−
1
+
45
Browse the problem library