JEE MATHEMATICS MCQ: INCREASING & DECREASING

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Analyzing +4 | -1

Let

f^{\prime}(\sin x) < 0

and

f^{\prime \prime}(\sin x) > 0

for all

x \in(0, \pi / 2)

and

g(x)=f(\sin x)+f(\cos x)

, then

g(x)

is decreasing in

View answer and explanation

Correct option: B

\left(0, \frac{\pi}{4}\right)

Option A

\left(\frac{\pi}{4}, \frac{\pi}{2}\right)

is incorrect. Option B

\left(0, \frac{\pi}{4}\right)

is correct because g'(x) is negative in this interval, indicating that g(x) is decreasing.

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