Find the equation of the normal toy = 2x3 – x2 + 3 at (1, 4).

1.	Find the equation of the normal toy = 2x3 – x2 + 3 at (1, 4).
Answer» finding the slope of the tangent by differentiating the curve \(m=\frac{dy}{dx}=6x^2-2x\) m = 4 at (1,4) normal is perpendicular to tangent so, m₁m₂ = – 1 \(m(normal)=-\frac{1}{4}\) equation of normal is given by y – y₁ = m(normal)(x – x₁) \(y-4=(-\frac{1}{4})(x-1)\) x + 4y = 17

Answer»

finding the slope of the tangent by differentiating the curve

\(m=\frac{dy}{dx}=6x^2-2x\)

m = 4 at (1,4)

normal is perpendicular to tangent so, m₁m₂ = – 1

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

equation of normal is given by y – y₁ = m(normal)(x – x₁)

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

x + 4y = 17

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