Let f: R \rightarrow R be a twice differentiable function such that f^{' '}(x)>0 for all x \in R and f^{'}(a-1)=0, where a is a real number. Let g(x)=f (\tan ^2 x-2 \tan x+a) , 0< x< \frac{\pi}{2}. Consider the following two statements: (I) g is increasing in (0, \frac{\pi}{4}) (II) g is decreasing in (\frac{\pi}{4}, \frac{\pi}{2}) Then, [21 Jan 2026 Shift 2]

Correct Answer is : Neither (I) nor (II) is True

Application of Derivatives Part 3

Section: Mathematics

Question : 6 of 30

Marks: +1, -0

Let f:R⟶R be a twice differentiable function such that f′′(x)>0 for all x∈R and f′(a−1)=0, where a is a real number.
Let g(x)=f(tan2x−2‌tan‌x+a),0<x<‌

.
Consider the following two statements:
(I) g is increasing in (0,‌

)
(II) g is decreasing in (‌

,‌

) Then,

[21 Jan 2026 Shift 2]

Both (I) and (II) are True
Neither (I) nor (II) is True
Only (I) is True
Only (II) is True

Validate

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