x only exsists from [0,3.14] therefore what is the parallel tangent lines between f(x)=tanx and g(x)=x^2
What a nasty and tough question.
I read it that you want tangents to each curve, which are parallel to each other.
f'(x) = sec^2x and g'(x) = 2x
so sec^2 x = 2x
I will admit that I used Wolfram and I found that x = 2.0828
http://www.wolframalpha.com/input/?i=1%2F%28cos%28x%29%29%5E2+%3D+2x
so for the parabola
f(2.0828) = 4.338 and m = 4.1656
y - 4.338 = 4.1656(x-2.0828)
y = 4.1656x -4.338
------ this is the equation of the tangent to f(x) = x^2
when x = 2.0828 , g(2.0828) = -1.779
y + 1.779 = 4.1656(x-2.0828)
y = 4.1656x -10.4555
-----> this is the equation of the tangent to the tangent curve