Question:
Find the equation of the tangent and the normal to the following curves at the indicated points:
Solution:
finding the 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 $(0,5)=-10$
$\mathrm{~m}$ (normal) at $(0,5)=\frac{1}{10}$
equation of tangent is given by $y-y_{1}=m($ tangent $)\left(x-x_{1}\right)$
$y-5=-10 x$
$y+10 x=5$
equation of normal is given by $y-y_{1}=m($ normal $)\left(x-x_{1}\right)$
$y-5=\frac{1}{10} x$
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