Published by:
CGP EDU Academic Team
Published on: August 13, 2026
Let 
be a differentiable function such that
,
for all x > 0, where c is an arbitrary constant. Then
A
g is decreasing in 
B
g ’ is increasing in 
C
g + g' is increasing in 
D
g - g' is increasing in 
Text Solution
Verified by ExpertsThe correct answer is:
D
On differentiating both sides w.r.t. x, we get
g (x) is increasing in 
g"(x) = -sinx-cosx<0
g' (x) is decreasing function
let h (x) = g (x) + g' (x) = 2 cos x + C
h' (x) = g' (x) + g" (x) = - 2 sinx < 0
h is decreasing
let 
(x) = g (x) - g' (x) = 2 sin x + C
' (x) = g' (x) - g" (x) = 2 cos x > 0
is increasing
Hence option D is correct.
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