RD Sharma - Mathematics (Volume 1)

Book: RD Sharma - Mathematics (Volume 1)

Chapter: 17. Increasing and Decreasing Functions

Subject: Maths - Class 12th

Q. No. 26 of MCQ

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Mark the correct alternative in the following:

Let ϕ(x) = f(x) + f(2a – x) and f’’(x) > 0 for all xϵ[0, a]. The, ϕ(x)

Formula:- (i) 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)

ϕ(x) = f(x) + f(2a – x)

ϕ(x) = f’(x)-f’(2a – x)

ϕ’’(x) = f’’(x) + f’’(2a – x)

checking the condition

ϕ(x) is decreasing in [0,a]

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