Applications Of Derivatives Question 51
Question: Let $ g(x)=2f( \frac{x}{2} )+f(2-x) $ and $ f’’(x)<0\forall x\in (0,2) $ . Then g(x) increases in
Options:
A) (1/2, 2)
B) (4/3, 2)
C) (0, 2)
D) (0, 4/3)
Show Answer
Answer:
Correct Answer: D
Solution:
[d] We have $ g’(x)=f’( \frac{x}{2} )-f’(2-x) $ Given $ f’’(x)<0\forall \in (0,2) $
So, $ f’(x) $ is decreasing on (0, 2). Let $ \frac{x}{2}>2-x $ or $ f’( \frac{x}{2} )<f’(2-x) $ .
Thus, $ \forall x>\frac{4}{3},g’(x)<0 $ .
Therefore, $ g(x) $ decreasing in $ ( \frac{4}{3},2 ) $ and increasing in $ ( 0,\frac{4}{3} ) $ .
BETA
