JEE MATHEMATICS MCQ: INCREASING & DECREASING

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Analyzing +4 | -1

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

View answer and explanation

Correct option: D

K > 2

Option D (

K > 2

) is correct because for the function to be increasing, its derivative must be greater than 0, leading to the condition K > 2.

More Questions from INCREASING & DECREASING

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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)

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

\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

x > 0,

c