Find all points of the graph of y=7x^2+7x whose tangent lines are perpendicular to the line -49y=x

Answer 1

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

Answer 2

-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)

See

http://www.wolframalpha.com/input/?i=plot+y%3D7x%5E2%2B7x,+y%3D49(x-3)%2B84+for+x%3D0..5