Question

What is the equation of the line normal to `f(x)=2x^3 - x^2-x` at `x=4`?

Answer 1

`R(x) = {4-x}/87 + 108`

Explanation:

`f(4) = 2 * 64 - 16 - 4 = 128 - 20 = 108`

`f'(x) = 6x ^2 - 2x - 1`

`f'(4) = 6*16-8-1=96-9=87`

`R(x) = -1/87 x + b` is the desired perp.

`R(4) = 108 Leftrightarrow -4/87 + b = 108`

`b = 108 + 4/87`