JEE MATHEMATICS MCQ: INCREASING & DECREASING

1 Easy

1 of 1

Analyzing +4 | -1

f\left( x \right) = \frac{{a\sin x + b\cos x}}{{c\sin x + d\cos x}}

is decreasing for all

x

, then

View answer and explanation

Correct option: B

ad - bc < 0

Option B (

ad - bc < 0

) is correct because for the function to be decreasing, its derivative must be negative, leading to this condition on the coefficients.

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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)