dy/dx = slope = 1 - x/250
y = m x + 20
at tangent point
y = (1-x/250) x + 20 = x - x^2/500
solve that for x
Line l is tangent to the graph of
y= x - x²/500 at point Q & it crosses the y-axis at (0, 20)
a). Find the x-coordinate of point Q
b. Write an equation for line l
c) Suppose the graph of y=x-x^2/500, where x and y are measured in feet, represents a hill. There is a 50-foot tree growing vertically at the top of the hill. Does a spotlight at point P (point P is where line l crosses the x-axis) directed along the line l shine on any part of the tree? Show the work that leads to your conclusion.
1 answer
3 answers