Find the equation of the normal to `y=2x^3-x^2+3` at (1,4).

Explanation

y=`2 x^{3}-x^{2}+3`


Differentiate both sides w.r.t.`x`,

`Rightarrowfrac{dy}{dx}=6x^2-2x`

`Rightarrowtext { Slop of tangent }=(frac{dy}{dx})_{(1,4)}=6(1)^{2}-2(1)=6-2=4`

`Rightarrowtext{ Slop of normal}=frac{-1}{text { Slop of tangent }}=frac{-1}{4}`


`Rightarrow(x_{1},y_{1})=(1,4)quadtext { [Given ] }`

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