If the normal to the curve y=f(x) at the poin | vedclass

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(B) The slope of the normal to the curve $y=f(x)$ at a point is given by $m_n = 	an(	heta)$,where $	heta$ is the angle made with the positive $X$-a

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$1$

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(B) The slope of the normal to the curve $y=f(x)$ at a point is given by $m_n = 	an(	heta)$,where $	heta$ is the angle made with the positive $X$-axis.Given $	heta = \frac{3 \pi}{4}$,the slope of the normal is $m_n = 	an\left(\frac{3 \pi}{4}ight) = -1$.We know that the slope of the normal is also related to the derivative of the function by the formula $m_n = -\frac{1}{f^{\prime}(x)}$.At the point $(3,4)$,we have $m_n = -\frac{1}{f^{\prime}(3)}$.Equating the two expressions for the slope of the normal:$-1 = -\frac{1}{f^{\prime}(3)}$$f^{\prime}(3) = 1$.

If the normal to the curve $y=f(x)$ at the point $(3,4)$ makes an angle $\left(\frac{3 \pi}{4}\right)^{C}$ with the positive $X$-axis,then $f^{\prime}(3)$ is equal to

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