The question from my textbook:
Find the equation of the tangent line to the curve $y = x²-2x$ that is perpendicular to the line $x-2y = 1$
- The derivative of the parabola: $2x-2$
- It's normal slope of the tangent: $-2$
I thought of doing
1.
$-2x-2 = \frac x 2 - \frac 1 2$
$-2.5 x + 1.5 = 0$
Root : $\frac 35 = 0.6$
then
$y-0 = -2 (x-0.6)$ $y = -2x -0.6$
but is clearly false and the right answer would be $y = -2x$ but how to find it?
2. (I also thought of doing $-2 = 2x - 2$, then it would explain the $0$ for x-axis and for y-axis if insert to the parabola, is it the right way to do it?)
Can someone help me? I would love to know the steps behind the resolution of the problem