Find the equation


Find the equation of the tangent and the normal to the following curves at the indicated points:

$y=x^{4}-6 x^{3}+13 x^{2}-10 x+5$ at $x=1 y=3$


finding slope of the tangent by differentiating the curve

$\frac{d y}{d x}=4 x^{3}-18 x^{2}+26 x-10$

$\mathrm{m}$ (tangent) at $(\mathrm{x}=1)=2$

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

$\mathrm{m}$ (normal) at $(\mathrm{x}=1)=-\frac{1}{2}$

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


$y=2 x+1$

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


$2 y=7-x$

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