Determine the equation (s) of tangent (s) line to the curve y = 4x³ – 3x + 5 which are perpendicular to the line 9y + x + 3 = 0.

finding the slope of the tangent by differentiating the curve

m(tangent) =

the slope of given line is , so the slope of line perpendicular to it is 9

x = 1 or – 1

since this point lies on the curve, we can find y by substituting x

y = 6 or 4

therefore, the equation of the tangent is given by

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

y – 6 = 9(x – 1)

or

y – 4 = 9(x + 1)