Let $f(x)$ be a function defined by $f(x)=\left(a b-a^2-2\right) x-\int_\limits 0^x\left(\cos ^4 t+\sin ^2 t-2\right) d t$ If $f(x)$ is a decreasing function for all $x \in R$ and $a \in R$, where $a$ is independent of $x$, then

JEE MATHEMATICS MCQ: INCREASING & DECREASING

1 Easy

1 of 1

Analyzing +4 | -1

Let

f(x)

be a function defined by

f(x)=\left(a b-a^2-2\right) x-\int\limits_{0}^x\left(\cos ^4 t+\sin ^2 t-2\right) d t

f(x)

is a decreasing function for all

x \in R

and

a \in R

, where

a

is independent of

x

, then

View answer and explanation

Correct option: D

None of these

The correct answer is D (None of these) because the condition for

f(x)

to be decreasing leads to

b \in(-\sqrt{3}, \sqrt{3})

, which is not covered by the other options.