1
You visited us
1
times! Enjoying our articles?
Unlock Full Access!
Byju's Answer
Standard XII
Mathematics
Modulus Function
If f x = x 3+...
Question
If f(x) = x
3
+ ax
2
+ bx + c has a maximum at x=
-
1 and minimum at x=3. Determine a,b and c.
Open in App
Solution
Given
:
y
=
x
3
+
a
x
2
+
b
x
+
c
⇒
d
y
d
x
=
3
x
2
+
2
a
x
+
b
S
ince
f
x
is at maximum at
x
=-1 and minimum at
x
=3
,
x
=
-
1
and
x
=
3
are
the
critical
points
.
At
x
=
-
1
:
d
y
d
x
=
3
-
1
2
+
2
a
-
1
+
b
=
0
⇒
3
-
2
a
+
b
=
0
⇒
2
a
-
b
=
3
.
.
.
1
At
x
=
3
:
d
y
d
x
=
3
3
2
+
2
a
3
+
b
=
0
⇒
27
+
6
a
+
b
=
0
⇒
-
6
a
-
b
=
27
.
.
.
2
From eqs.
1
and
2
, we get
a
=
-
3
,
b
=
-
9
and
c
∈
R
Suggest Corrections
0
Similar questions
Q.
If
f
(
x
)
=
x
3
+
a
x
2
+
b
x
+
c
is minimum at
x
=
3
and maximum at
x
=
−
1
Q.
lf
f
(
x
)
=
x
3
+
a
x
2
+
b
x
+
c
has a maximum at
x
=
−
1
and minimum at
x
=
3
, then
Q.
f
(
x
)
=
x
3
+
a
x
2
+
b
x
+
c
has a max. at
x
=
−
1
and min. at
x
=
3
. Determine the constants
a
,
b
,
c
.
Q.
Suppose for fixed real numbers a and b.
f
(
x
)
=
x
3
+
a
x
2
+
b
x
+
c
, has 3 distinct roots for c =0. Then
Q.
Suppose
f
(
x
)
=
x
3
+
a
x
2
+
b
x
+
c
satisfies
f
(
–
2
)
=
−
10
and takes the extreme value
50
27
at
x
=
2
3
.
Then the value of
a
+
b
+
c
is
View More
Join BYJU'S Learning Program
Grade/Exam
1st Grade
2nd Grade
3rd Grade
4th Grade
5th Grade
6th grade
7th grade
8th Grade
9th Grade
10th Grade
11th Grade
12th Grade
Submit
Related Videos
Some Functions and Their Graphs
MATHEMATICS
Watch in App
Explore more
Modulus Function
Standard XII Mathematics
Join BYJU'S Learning Program
Grade/Exam
1st Grade
2nd Grade
3rd Grade
4th Grade
5th Grade
6th grade
7th grade
8th Grade
9th Grade
10th Grade
11th Grade
12th Grade
Submit
AI Tutor
Textbooks
Question Papers
Install app