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Question 5 - Week 8 Practice | Prasnya
Q5
00:00
16 Mar 2025
Q5.
Consider the function
f
:
R
→
R
f:\mathbb{R}\to\mathbb{R}
f
:
R
→
R
defined by
f
(
x
)
=
{
x
2
−
∣
x
∣
,
x
<
0
,
x
2
+
∣
x
∣
,
x
≥
0.
f(x)=\begin{cases}x^2-|x|, & x<0,\\ x^2+|x|, & x\ge0.\end{cases}
f
(
x
)
=
{
x
2
−
∣
x
∣
,
x
2
+
∣
x
∣
,
x
<
0
,
x
≥
0.
Which of the following option(s) is(are) correct?
A
f
f
f
is not differentiable at
x
=
0
x=0
x
=
0
.
B
f
f
f
is continuous at
x
=
0
x=0
x
=
0
.
C
f
f
f
is differentiable at
x
=
1
x=1
x
=
1
.
D
f
f
f
is not continuous at
x
=
1
x=1
x
=
1
.
Save
Check
Details
Q5
00:00
16 Mar 2025
Q5.
Consider the function
f
:
R
→
R
f:\mathbb{R}\to\mathbb{R}
f
:
R
→
R
defined by
f
(
x
)
=
{
x
2
−
∣
x
∣
,
x
<
0
,
x
2
+
∣
x
∣
,
x
≥
0.
f(x)=\begin{cases}x^2-|x|, & x<0,\\ x^2+|x|, & x\ge0.\end{cases}
f
(
x
)
=
{
x
2
−
∣
x
∣
,
x
2
+
∣
x
∣
,
x
<
0
,
x
≥
0.
Which of the following option(s) is(are) correct?
A
f
f
f
is not differentiable at
x
=
0
x=0
x
=
0
.
B
f
f
f
is continuous at
x
=
0
x=0
x
=
0
.
C
f
f
f
is differentiable at
x
=
1
x=1
x
=
1
.
D
f
f
f
is not continuous at
x
=
1
x=1
x
=
1
.
Save
Check
Details
