The green line represents f(x) = (x^2)*sqrt(3) - 1 and red one represents a line which you only know the slope of which is sqrt(3). And for the purpose of my question you can ignore the values in the plot. And my question is how do you compute A (the point at which the red line intercests do green one) knowing that the red line is tangent to the green line at A, without using a derivative?

And without using math more advanced than 11th grade geometry.

And here is the plot:

http://i134.photobucket.com/albums/q...nsilv/plot.jpg