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if the function f(x)=2tanx+(2a+1)ln|secx|+(a-2)x is increased on R then find interval to which a belongs?

if the function f(x)=2tanx+(2a+1)ln|secx|+(a-2)x is increased on R then find interval to which a belongs?

Grade:12

1 Answers

bharat bajaj IIT Delhi
askIITians Faculty 122 Points
6 years ago
f`(x) = 2sec^{2} x+ (2a+1) tan x + (a-2)
f`(x) > 0 if the function is increasing on R.
THe first term is always positive.
For f`(x) > 0,
As tan x can vary from (-inf, +inf)
Hence, the interval of a should be (-inf,+inf) for f`(x) to be greater than 0
Thanks&Regards
Bharat Bajaj
askiitian faculty
IIT Delhi

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