Application of DerivativeMedium
Question
Let the function g: (- ∞, ∞) → 
be given by g(u) = 2tan-1(eu) - 
. Then, g is
be given by g(u) = 2tan-1(eu) - . Then, g isOptions
A.even and is strictly increasing in (0, ∞)
B.odd and is strictly decreasing in (-∞, ∞)
C.odd and is strictly increasing in (-∞, ∞)
D.neither even nor odd, but is strictly increasing in (-∞, ∞)
Solution
g(u) = 2 tan-1(eu)-
= 2tan-1 eu - tan-1 eu - cot-1 eu = tan-1 eu - cot-1 eu
g(-x) = -g(x)
⇒ g(x) is odd
and g′(x) > 0 ⇒ increasing.
= 2tan-1 eu - tan-1 eu - cot-1 eu = tan-1 eu - cot-1 eu
g(-x) = -g(x)
⇒ g(x) is odd
and g′(x) > 0 ⇒ increasing.
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