Published by:
CGP EDU Academic Team
Published on: August 13, 2026
Consider the following three statements for the function 
defined by 
:
(I) 
is differentiable at all 
.
(II) 
is increasing in 
.
(III) 
is decreasing in 
.
Then.
Text Solution
Verified by ExpertsThe correct answer is:
D
For 
: 
, 
(decreasing).
For 
: 
(decreasing).
At 
: LHD 
. So 
is differentiable at 
.
(I) TRUE: 
is differentiable for all 
.
(II) FALSE: 
is decreasing in 
.
(III) TRUE: 
is decreasing in 
.
Only (I) and (III) are TRUE.
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