Q. 84.0( 2 Votes )

Mark the correct A.

B.

C.

D.

Answer :

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



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