🛠️ JEE➗ Maths

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

\(
\text { If }-1<x<2 \text {, then }|f(x)-g(x)|<8
\)

c

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

d

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

🔒
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