JEE MATHEMATICS MCQ: INCREASING & DECREASING

1 Easy

1 of 1

Analyzing +4 | -1

g(x)

is a continuous function at

x=a

such that

g(a) > 0

and

f^{\prime}(x)=g(x)\left(x^2-a x+a^2\right)

for all

x \in R

, then

f(x)

, is

View answer and explanation

Correct option: A

Increasing in the neighbourhood of

x=a

Option A (Increasing in the neighbourhood of

x=a

) is correct because

f'(x) > 0

in the neighborhood of

x=a

, indicating that

f(x)

is increasing.

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f\left( x \right) = \frac{{K\sin x + 2\cos x}}{{\sin x + \cos x}}

x

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a

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f

g

fog

f\left( x \right) = {x^3} + b{x^2} + cx + d

0 < {b^2} < c

\left( { - \infty ,\;\infty } \right)