At what point of the curve y= x^4 is the normal line parallel to 2x + y = 3? Find the equation of the normal line.

Answer 1

the normal line is perpendicular to the tangent

the slope of the tangent is the 1st derivative

normal slope ... -2
tangent slope ... 1/2

1/2 = 4 x^3
... 1/8 = x^3
... 1/2 = x

point ... (1/2 , 1/16)

equation ... y - 1/16 = -2 (x - 1/2)