Find the equations of the tangent and the normal to the curve `y=x^2+4x+1` at `x=3` at the indicated points

Answer

Equation of tangent is `10 x-y-8=0
`

Equation of normal is `x+10 y-223=0`

Explanation

ATQ,

`y=x^{2}+4 x+1`

Differentiating both sides w.r.t.`x`,
$$ \frac{d y}{d x}=2 x+4 $$
When `x=3, y=9+12+1=22`

So,`(x_{1}, y_{1})=(3,22)`

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