Find an equation of the tangent to the curve f(x) = 2x^2 - 2x + 1 that has slope 2.

Answer 1

f' = slope = 4 x -2
so
4x-2 = 2
4 x = 4
x = 1
if x = 1 then
y = 2 -2 + 1 = 1
so tangent at point (1,1) and m = 2
1 = 2 (1) + b
b = -1
so
y = 2 x - 1