JEE MATHEMATICS MCQ: INCREASING & DECREASING

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Analyzing +4 | -1

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

and

f^{\prime}(1)=0

such that

g(x)=f\left(\cot ^2 x+2 \cot x+2\right)

, where

0 < x < \pi

, then the interval in which

g(x)

is decreasing is

View answer and explanation

Correct option: D

\left(0, \frac{3 \pi}{4}\right)

Option D is correct because

g'(x) < 0

for

x \in (0, \frac{3\pi}{4})

, indicating that

g(x)

is decreasing in this interval.

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f\left( x \right) = \frac{{K\sin x + 2\cos x}}{{\sin x + \cos x}}

x

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a

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f

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fog

f\left( x \right) = {x^3} + b{x^2} + cx + d

0 < {b^2} < c

\left( { - \infty ,\;\infty } \right)