JEE MATHEMATICS MCQ: INCREASING & DECREASING

1 Easy

1 of 1

Analyzing +4 | -1

Let

g(x)=2 f\left(\frac{x}{2}\right)+f(2-x)

and

f^{\prime \prime}(x) < 0

for all

x \in(0,2)

. Then,

g(x)

, is

View answer and explanation

Correct option: C

Increasing on

(0,4 / 3)

and decreasing on

(4,3,2)

Option C (Increasing on

(0,4 / 3)

and decreasing on

(4,3,2)

) is correct because

g'(x)

is positive on

(0, 4/3)

and negative on

(4/3, 2)

, indicating increasing and decreasing behavior respectively.

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