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Let $f(x)$ be a differentiable function, $A(0, \alpha)$ and $B(8, \beta)$ be two points on the curve $y=f(x)$. Given $f(0)=2$ and $f^{\prime}(4)=\frac{-3}{4}$. If the chord $A B$ of the curve is parallel to the tangent drawn at the point $(4, \mathrm{f}(4))$, then $\beta=$
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The correct answer is:
-4
Point $A(0, \alpha)$ is on $y=f(x)$ $\therefore f(0)=\alpha$
and also given $f(0)=2$
Therefore $\alpha=2$.
Since slope of chord $A B=$ Slope of tangent on $y=f(x)$ at $x=4$ $\Rightarrow \frac{\beta-\alpha}{8-0}=f^{\prime}(4)$
$\begin{aligned} & \Rightarrow \frac{\beta-2}{8}=-\frac{3}{4} \\ & \Rightarrow \beta=-4\end{aligned}$
and also given $f(0)=2$
Therefore $\alpha=2$.
Since slope of chord $A B=$ Slope of tangent on $y=f(x)$ at $x=4$ $\Rightarrow \frac{\beta-\alpha}{8-0}=f^{\prime}(4)$
$\begin{aligned} & \Rightarrow \frac{\beta-2}{8}=-\frac{3}{4} \\ & \Rightarrow \beta=-4\end{aligned}$
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