Find the equation
Question:

Find the equation of the normal toy $=2 x^{3}-x^{2}+3$ at $(1,4)$.

Solution:

finding the slope of the tangent by differentiating the curve

$\mathrm{m}=\frac{\mathrm{dy}}{\mathrm{dx}}=6 \mathrm{x}^{2}-2 \mathrm{x}$

$\mathrm{m}=4$ at $(1,4)$

normal is perpendicular to tangent so, $m_{1} m_{2}=-1$

$\mathrm{m}($ normal $)=-\frac{1}{4}$

equation of normal is given by $y-y_{1}=m($ normal $)\left(x-x_{1}\right)$

$y-4=\left(-\frac{1}{4}\right)(x-1)$

$x+4 y=17$

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