Finding Equations of Normal Lines Parallel to a Given Line

[SherlockOhms]

Homework Statement

Find the equation of each of the normal lines to the curve y = x^3 - 4x that is parallel to the line x + 8y - 8 = 0.

Homework Equations

Differentiation, y - y1 = m(x - x1)

The Attempt at a Solution

Well, clearly I start by differentiating y = x^3 - 4x to gey dy/dx = 3x^2 - 4. Then, this is the slope of the tangent to the graph y. This slope is equal to the slope of the line x + 8y - 8 = 0. Which is -8. So, I then evaluate for x and sub back into dy/dx, giving me the slope of the tangent. The slope of the normal line is the negative reciprocal of this. If you solve for x using
3x^2 - 4 = -8, you get an imaginary value though. Where have I gone wrong?

 

[CAF123]

You have the gradient of the given line wrong.

 

[SherlockOhms]

You have the gradient of the given line wrong.

Cool. See where I went wrong now. Stupid slip.