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

Question

Let $f$ and $g$ be the twice differentiable functions on $\mathbb{R}$ such that

$f''(x)=g''(x)+6x$

$f'(1)=4g'(1)-3=9$

$f(2)=3g(2)=12$.

Then which of the following is NOT true?

$g(-2)-f(-2)=20$

There exists $x_0\in(1,3/2)$ such that $f(x_0)=g(x_0)$

$|f'(x)-g'(x)| < 6\Rightarrow -1 < x < 1$

If $-1 < x < 2$, then $|f(x)-g(x)| < 8$

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