JEE MATHEMATICS MCQ: INCREASING & DECREASING

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Analyzing +4 | -1

f(x)=\left(a b+b^2+1\right) x+\int\limits_{0}^x\left(\cos ^4 \theta+\sin ^4 \theta\right) d \theta

is an increasing function of

x

for all

x \in R

and

b \in R, b

being independent of

x

, then

View answer and explanation

Correct option: B

a \in(-\sqrt{6}, \sqrt{6})

Option B (

a \in(-\sqrt{6}, \sqrt{6})

) is correct because it ensures that the derivative of

f(x)

is always positive, making

f(x)

an increasing function.

More Questions from INCREASING & DECREASING

Practice All Chapter MCQs →

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

x

f\left( x \right) = {x^2} + ax + 1

a

f(x)=

\sin x-\cos x-a x+b

f(x)=x e^{x(1-x)}, x \in R

f

g

fog

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

0 < {b^2} < c

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