Question
Question: L'' (x) \> 0 " x Ī R and g(x) = f(2 – x) + f(4 + x). Then g(x) is increasing in –...
L'' (x) > 0 " x Ī R and g(x) = f(2 – x) + f(4 + x).
Then g(x) is increasing in –
A
(– , – 1)
B
(– , 0)
C
(– 1, )
D
None
Answer
(– 1, )
Explanation
Solution
f '' (x) > 0 " x Ī R Ž f ' (x) is increasing " x Ī R
g ' (x) = – f ' (2 – x) + f ' (4 + x)
If g ' (x) > 0, then
f ' (4 + x) > f ' (2 – x)
Ž 4 + x > 2 – x
2x > – 2
x > – 1 Ž (–1, )
g(x) is increasing in (–1, )