Let f and g be twice differentiable functions on ℝ such that f''(… | JEE Main 2023 Mathematics PYQ

MCQMediumJEE Main 2023 · 29 January, Shift 2Linear Differential Equations

Let $f$ and $g$ be twice differentiable functions on $\mathbb{R}$ such that $f''(x) = g''(x) + 6x$ , $f'(1) = 4g'(1) - 3 = 9$ , and $f(2) = 3g(2) = 12$ . Which of the following is NOT true?

A
$g(-2) - f(-2) = 20$
B
If $-1 < x < 2$ , then $|f(x) - g(x)| < 8$
C
$|f'(x) - g'(x)| < 6, -1 < x < 1$
D
There exists $x_0 \in \left[1, \frac{3}{2}\right]$ such that $f(x_0) = g(x_0)$

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