NCERT Exemplar - MCQs

Chapter 6 Class 12 Application of Derivatives
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## (D) sometimes increases and sometimes decreases.

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This question is similar to Question 32 CBSE Class 12 Sample Paper 2021 Boards - Application of Derivatives

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### Transcript

Question 22 The function f (x) = tan x β x always increases (B) always decreases (C) never increases (D) sometimes increases and sometimes decreases. Given π(π₯) = tan π₯ β π₯ Finding π^β² (π) π^β² (π₯)=γπππγ^π π βπ Now, we need to check if π(π) is increasing or decreasing Checking sign of π^β² (π) π^β² (π₯)=γπππγ^π π βπ Now, π¬ππ π π (ββ,βπ]βͺ[π,β) So, γπππγ^π π π [1,β) Therefore, we can write this as πβ€γπππγ^π πβ€β 1βπβ€γπ ππγ^2 π₯βπβ€ββπ 0β€γπππγ^π πβπβ€β Thus, γπ ππγ^2 π₯β1β₯0 β΄ π^β² (π)>π for all values of x Hence, π(π) always increases. So, the correct answer is (A)