JEE MATHEMATICS MCQ: INCREASING & DECREASING

1 Easy

1 of 1

Application +4 | -1

The value of

a

in order that

f(x)=

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

decreases for all real values is given by

View answer and explanation

Correct option: A

a \geq \sqrt{2}

Option A (

a \geq \sqrt{2}

) is correct because it ensures that the derivative of the function is always negative, indicating that the function is decreasing for all real values.

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 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)

Let

g:\,(0,\infty ) \to R

be a differentiable function such that

\int {\left( {\frac{{x(\cos x - \sin x)}}{{{e^x} + 1}} + \frac{{g(x)\left( {{e^x} + 1 - x{e^x}} \right)}}{{{{\left( {{e^x} + 1} \right)}^2}}}} \right)} dx = \frac{{xg(x)}}{{{e^x} + 1}} + c

, for all

x > 0,

where

c

is an arbitrary constant. Then: