RD Sharma - Mathematics (Volume 1)

Book: RD Sharma - Mathematics (Volume 1)

Chapter: 17. Increasing and Decreasing Functions

Subject: Maths - Class 12th

Q. No. 8 of MCQ

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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)


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)


For increasing function


2tan2x+2atanx+tanx+ a>0

From formula (i)


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