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Let \(f\) and \(g\) be twice differentiable functions on \(R\) such that \( \begin{aligned} & f^{\prime \prime}(x)=g…

Q1

Let \(f\) and \(g\) be twice differentiable functions on \(R\) such that
\(
\begin{aligned}
& f^{\prime \prime}(x)=g^{\prime \prime}(x)+6 x \\
& f^{\prime}(1)=4 g^{\prime}(1)-3=9 \\
& f(2)=3 g(2)=12
\end{aligned}
\)

Then 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

\(\left|f^{\prime}(x)-g^{\prime}(x)\right|<6 \Rightarrow-1<x<1\)

d

There exists \(x_0 \in\left(1, \frac{3}{2}\right)\) such that \(f\left(x_0\right)=g\left(x_0\right)\)

🔒
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