Let g: R → R be a non constant twice differentiable function such that g^()(1/2)=g^()(3/2). If a real valued function f is defined as f(x)=1/2[g(x)+g(2-x)], then

(A) f^()(x)=0 for atleast two x in (0,2)

(C) f^()(x)=0 for no x in (0,1)

(D) f^()(x)=0 for exactly one x in (0,1)

Limit, Continuity and Differentiability: JEE Main 2024 Mathematics question

JEE Main 2024 · 30 Jan, Morning shift · Q3702

JEE Main 202430 Jan, Morning shiftMathematicsMediumLimit, Continuity and Differentiability420× since 2002

Let

g: \mathbf{R} \rightarrow \mathbf{R}

be a non constant twice differentiable function such that

\mathrm{g}^{\prime}\left(\frac{1}{2}\right)=\mathrm{g}^{\prime}\left(\frac{3}{2}\right)

. If a real valued function

f

is defined as

f(x)=\frac{1}{2}[g(x)+g(2-x)]

, then