Let g: ℝ → ℝ be a non-constant twice differentiable function such… | JEE Main 2024 Mathematics PYQ

MCQMediumJEE Main 2024 · 30 January, Shift 1Differentiability

Let $g: \mathbb{R} \to \mathbb{R}$ be a non-constant twice differentiable function such that $g'\left(\frac{1}{2}\right) = g'\left(\frac{3}{2}\right)$ . If a real-valued function $f$ is defined as $f(x) = \frac{1}{2}[g(x) + g(2 - x)]$ , then:

A
$f''(x) = 0$ for at least two $x$ in $(0,2)$
B
$f''(x) = 0$ for exactly one $x$ in $(0,1)$
C
$f''(x) = 0$ for no $x$ in $(0,1)$
D
$f'\left(\frac{3}{2}\right) + f'\left(\frac{1}{2}\right) = 1$

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