Let f:R be a twice differentiable function such that f''(x)>0 for all x and f'(a-1)=0, where a is a real number. Let g(x)=f(tan ²x-2 tan x+a), 0<x<(π)/2. Consider the following two statements: (I) g is increasing in (0, (π)/4) (II) g is deceasing in ((π)/4, (π)/2) Then,

(A) Neither (I) nor (II) is True

Limit, Continuity and Differentiability: JEE Main 2026 Mathematics question

JEE Main 2026 · 21 Jan, Evening shift · Q11

JEE Main 202621 Jan, Evening shiftMathematicsMediumLimit, Continuity and Differentiability420× since 2002

Let

f:\mathbf{R}\to\mathbf{R}

be a twice differentiable function such that

f''(x)>0

for all

x\in\mathbf{R}

and

f'(a-1)=0

, where a is a real number. Let

g(x)=f(\tan^2x-2\tan x+a)

0<x<\frac{\pi}{2}

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

\left(0, \frac{\pi}{4}\right)

(II) g is deceasing in

\left(\frac{\pi}{4}, \frac{\pi}{2}\right)

Then,