Question:

At what point on the curve $\displaystyle y=-2x^4$ is the tangent line perpendicular to the line $\displaystyle x-y+1=0$?

What I did was set the derivative of the curve ($\displaystyle -8x^3$) equal to the negative slope of the second (-1 in this case) as that's how I assumed we find the perpendicular line.

I got an answer of 2, but the book says $\displaystyle x=1/2$