JEE MATHEMATICS MCQ: INCREASING & DECREASING

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Application +4 | -1

If the function

\mathrm{f}(\mathrm{x})=\mathrm{x}^3+a \mathrm{x}^2+\mathrm{a}^2 \mathrm{x}+2 \sin ^2 \mathrm{x}

is strictly increasing

\forall \mathrm{x} \in \mathrm{R}

, then

a

View answer and explanation

Correct option: D

\mathrm{R}-(-\sqrt{3}, \sqrt{3})

Option D (

\mathrm{R}-(-\sqrt{3}, \sqrt{3})

) is correct because the derivative of the function must be greater than 0 for all x, which leads to the condition

a^2 \geq 3

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)