The equation of the tangent to the curve y = x^2 - 2x that is perpendicular to the line 2y = x - 1 has to be found.
The line 2y = x - 1 can be written in the slope intercept form as y = (1/2)*x - 1/2. A line perpendicular to this has a slope -1/(1/2) = -2
For a function f(x), the value of f'(a) gives the slope of the tangent at the point x = a.
y = x^2 - 2x
y' = 2x - 2
If 2x - 2 = -2, x = 0 and subsequently y = 0
This gives the equation of the tangent as y/x = -2
=> y + 2x = 0
The equation of the tangent to the curve y=x^2 - 2x that is perpendicular to the line 2y = x - 1 is y + 2x = 0