Find the equation of the tangent to the curve y=3x^2+4x which makes a 45 degree angle with the negative x-axis
the indicated line has slope -1.
y' = 6x+4
6x+4 = -1 when x = -5/6
y(-5/6) = -5/4
So, the line is
y = -(x+5/6) - 5/4
http://www.wolframalpha.com/input/?i=plot+y%3D3x^2%2B4x%2C+y+%3D+-%28x%2B5%2F6%29+-+5%2F4