JEE MATHEMATICS MCQ: INCREASING & DECREASING

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Analyzing +4 | -1

The set of all values of the parameter

a

for each of which the function

f(x)=\sin 2 x-8(a+1) \sin x+\left(4 a^2+8 a-14\right) x

increases for all

x \in \mathbb{R}

and has no critical points is

View answer and explanation

Correct option: A

(-\infty,-2-\sqrt{5}) \cup(\sqrt{5}, \infty)

Option A is correct because the given condition leads to a quadratic expression that must be positive for all x, resulting in the specified range for 'a'.

More Questions from INCREASING & DECREASING

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If the function

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

is increasing for all values of

x

, then The set of values of a for which the function

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

is an increasing function on [1,2] is The value of

a

in order that

f(x)=

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

decreases for all real values is given by The function

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

, is If

f

and

g

are two increasing functions such that

fog

is defined, then If

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

and

0 < {b^2} < c

, then in

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