Question

Line L is tangent to the graph of y= x- (x^2/500) at the point Q
a) find the x coordinate of point Q
B) right an equation for line L
C) suppose the graph above were a hill (measured in feet). There is a 50 foot tree growing vertically at the top of the hill. Does a spot light (a point P, on the x axis along the line L) shine on any part of the tree?

Answer 1

Did you want that tangent to be horizontal ?
if so, then

dy/dx = 1 - x/250

to be horizontal tangent, dy/dx = 0
x/250 = 1
x = 250
then y = 250 - (250^2)/500 = 125
Q is (250,125)

b) Did you mean" write" an equation for line L ?

Until you clarify your question, I will stop here.

Answer 2

they drew a diagram for it and Q is actually on the left side of the graph making the line L an upward slant, and yes i meant "write"