Differentiation - Tangents and Normals at a Point

Differentiation - Tangents and Normals at a Point

TGM Original Questions

Find the coordinates of the point(s) on the curve \(y = x(x^2 + 5) - 4\) where the tangent to the curve is parallel to \(y = 6x + 7\).

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Answer:\(\left(\dfrac{\sqrt3}{3},\dfrac{16\sqrt3-36}{9}\right)\) and \(\left(-\dfrac{\sqrt3}{3},-\dfrac{16\sqrt3+36}{9}\right)\)

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