JEE MATHEMATICS MCQ: INCREASING & DECREASING

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Analyzing +4 | -1

\phi \left( x \right)

is continuous at

x = \alpha

such that

\phi \left( \alpha \right) < 0

and

f\left( x \right)

is a function such that

f'\left( x \right) = \left( {ax - {a^2} - {x^2}} \right)\phi \left( x \right)

for all

x

, then

f\left( x \right)

View answer and explanation

Correct option: A

Increasing in the neighbourhood of

x = \alpha

Option A is correct because the derivative of the function, f'(x), is positive in the neighborhood of x = α, indicating that the function is increasing.

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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)