posted by Andrew .
Find all points of the graph of y=7x^2+7x whose tangent lines are perpendicular to the line -49y=x
y = -1/49 x
the slope of the perpendicular is
... -(-1/49) = 49
the 1st derivative is the slope of the tangent ... dy/dx = 14x + 7
14x + 7 = 49
find x, then find y from the original function
-49y=x has slope -1/49
so, you want lines with slope 49
since y' = 7(2x+1), that means x=3.
y(3) = 84
so, the line is
y-84 = 49(x-3)