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JEE Main Math Class 11 Straight Lines and Pair of Straight Lines 1 Questions
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© examsnet.com
Question : 9
Total: 100
Let
f
:
R
→
R
be defined as
f
(
x
)
=
{
x
5
sin
(
1
x
)
+
5
x
2
x
<
0
0
x
=
0
x
5
cos
(
1
x
)
+
λ
x
2
x
>
0
.
The value of
lambda
for which
f
" (0) exists, is ______.
[NA Sep. 06, 2020 (I)]
Your Answer:
Validate
Solution:
f
′
(
x
)
=
{
5
x
4
⋅
sin
(
1
x
)
−
x
3
cos
(
1
x
)
+
10
x
x
<
0
0
x
=
0
5
x
4
cos
(
1
x
)
+
x
3
sin
(
1
x
)
+
2
λ
x
x
>
0.
f
′
′
(
x
)
=
{
(
20
x
3
−
x
)
sin
(
1
x
)
−
8
x
2
cos
(
1
x
)
+
10
x
<
0
0
x
=
0
(
20
x
3
−
x
)
cos
(
1
x
)
+
8
x
2
sin
(
1
x
)
+
2
λ
x
>
0.
Now,
f
′
′
(
0
+
)
=
f
′
′
(
0
−
)
⇒
2
λ
=
10
⇒
λ
=
5
© examsnet.com
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