I'm lost on the sequence of doing this
Find the tangent and normal to the curves at the points indicated
y=2x^2-4x+1 where the gradient is 4
ok, so we know that the gradient of the normal line is -1/4. so let's tuck that away to use it later.
we are concerned with the point where $\displaystyle f'(x) = 4$, find that point. when you have that point, you can find the two lines using the point-slope form:
$\displaystyle y - y_1 = m(x - x_1)$
where $\displaystyle m$ is the slope of the line (m is 4 for the tangent and -1/4 for the normal) and $\displaystyle (x_1,y_1)$ is a point where the line passes through, namely, the point i asked you to find. now continue