Question
Question: Let f "(x) \> 0 ∀ x ∈ R and g(x) = f(2 – x) + f(4 + x). Then g(x) is increasing in...
Let f "(x) > 0 ∀ x ∈ 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 ∈ R ⇒ f '(x) is increasing ∀ x ∈ R.
g'(x) = −f '(2 − x) + f '(4 + x). If g'(x) > 0
⇒ f '(4 + x) > f'(2 - x)
⇒ 4 + x > 2 – x
⇒ x > −1