Fermi
·
Concept Library
·
Courses
·
Books
·
Problems
·
Simulations
·
Math Wiki
·
High School
Fermi
›
Problems
Mathematics
Mathematics
Problem
A quadratic polynomial
P
(
x
)
=
1
+
x
+
c
x
2
P(x)=1+x+cx^{2}
P
(
x
)
=
1
+
x
+
c
x
2
is intended to approximate
f
(
x
)
=
ln
(
1
+
x
)
f(x)=\ln(1+x)
f
(
x
)
=
ln
(
1
+
x
)
near
x
=
0
x=0
x
=
0
. Determine the value of
c
c
c
that ensures
P
P
P
and
f
f
f
have identical first and second derivatives at
x
=
0
x=0
x
=
0
. a)
−
1
2
-\dfrac12
−
2
1
b)
−
1
-1
−
1
c)
1
2
\dfrac12
2
1
d)
−
2
-2
−
2
Browse the problem library