Find the equation of normal line to the curve y = x³ + 2x + 6 which is parallel to the line x + 14y + 4 = 0.

finding the slope of the tangent by differentiating the curve

m(tangent) = 3x² + 2

normal is perpendicular to tangent so, m₁m₂ = – 1

m(normal) =

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

now comparing the slope of normal with the given equation

m(normal) =

x = 2 or – 2

hence the corresponding value of y is 18 or – 6

so, equations of normal are

Or