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If the normal to the curve $y=f(x)$ at $(3,4)$ makes an angle $\frac{3 \pi}{4}$ with the positive $x$-axis, then $f^{\prime}(3)$ is equal to
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Slope of the normal at $(3,4)$ is the value of
$\begin{array}{l}
-\frac{1}{f^{\prime}(x)} \text { at } x=3 \text { or }-\frac{1}{f^{\prime}(3)}=\tan \frac{3 \pi}{4}=1 \\
\Rightarrow f^{\prime}(3)=1
\end{array}$
$\begin{array}{l}
-\frac{1}{f^{\prime}(x)} \text { at } x=3 \text { or }-\frac{1}{f^{\prime}(3)}=\tan \frac{3 \pi}{4}=1 \\
\Rightarrow f^{\prime}(3)=1
\end{array}$
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