Question

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

Answer 1

The equation of the given curve is y = x³ + 2x + 6.

The slope of the tangent to the given curve at any point (x, y) is given by,

When x = 2, y = 8 + 4 + 6 = 18.

When x = −2, y = − 8 − 4 + 6 = −6.

Therefore, there are two normals to the given curve with slope -1/4 and passing through the points (2, 18) and (−2, −6).

Thus, the equation of the normal through (2, 18) is given by,