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Mark the correct alternative in the following:
If the function f(x) = 2tanx + (2a + 1) loge |sec x| + (a – 2) x is increasing on R, then
Formula:- (i) ax2+bx+c>0 for all x a>0 and b2-4ac<0
(ii) ax2+bx+c<0 for all x a<0 and b2-4ac<0
(iii) The necessary and sufficient condition for differentiable function defined on (a,b) to be strictly increasing on (a,b) is that f’(x)>0 for all x(a,b)
Given:-
f(x) = 2tanx+(2a+1)loge |sec x|+(a – 2)x
f’(x)=2sec2x+ (2a+1) tanx + (a-2)
f’(x)=2(tan2+1) + (2a+1).tanx +(a-2)
f’(x)=2tan2x+2atanx+tanx+a
For increasing function
f’(x)>0
2tan2x+2atanx+tanx+ a>0
From formula (i)
(2a+1)2-8a<0