Posted by **Aparna** on Sunday, January 27, 2013 at 9:40am.

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?

- Calc -
**Reiny**, Sunday, January 27, 2013 at 10:08am
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.

- Calc -
**Aparna**, Sunday, January 27, 2013 at 11:22am
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"

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