Let $c$ be a real number. What is the maximum value of $c$ such that the graph of the parabola $y = -6x^2$ has at most one point of intersection with the line $y = 5x+c?$
The line has a slope = 5
The slope at any point on the parabola = -12x
Set these =
-12x = 5
x = -5/12
So y= -6(-5/12)^2 = -25/24
So
-25/24 = 5 (-5/12) + c
25/12 - 25/24 = c
50/24 - 25/24 = c = 25/24
+456 
