JEE MATHEMATICS MCQ: INCREASING & DECREASING

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Application +4 | -1

The value of

a

in order that

f(x)=\sqrt{3} \sin x-\cos x-2 a x+b

decreases for all real value of

x

, is given by

View answer and explanation

Correct option: B

a \geq 1

Option B (

a \geq 1

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

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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)