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Manipal Entrance Test 2019 Math Paper
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© examsnet.com
Question : 15
Total: 70
If
f
(
x
)
=
{
x
0
≤
x
≤
1
2
x
−
1
1
<
x
, then
f is discontinuous at x = 1
f is differentiable at x = 1
f is continuous but not differentiable at x = 1
None of the above
Validate
Solution:
Given that,
f
(
x
)
=
{
x
0
≤
x
≤
1
2
x
−
1
1
<
x
From graph
f
(
x
)
is continuous,
∀
x
∈
R
i.e.
f
′
(
x
)
=
1
when
0
≤
x
≤
1
and
f
′
(
x
)
=
2
−
0
when
x
>
1
∴ Left hand limit ≠ Right hand limit
∴ At x = 1, f(x) is continuous but not differentiable.
© examsnet.com
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