The given curve is
y = 4x3 - 3x + 5
Let the required normal be at (x1, y1)
Slope of the tangent = dy/dx = 12x2 - 3
m2 = Slope of the line = 9
Since normal is perpendicular to the line.
Therefore, m1: m2 = –1
Hence, the points are (1, 6) and (–1, 4)
Equations of normals are:
