At what point(s) does the graph of the function shown below have a horizontal tangent? x^2+
y^2=2x There is a horizontal tangent at the point(s) . (Type an ordered pair. Use a comma to
separate answers as needed.)
Solution
x^2 + y^2 = 2x
by differentiating with respect to x we get
2x + 2y dy/dx = 2
dy/dx= 1-x/y
for a horizontl tangent the slope is zero.
1-x =0
x = 1.
so at points (1.1) and (1,-1) the tangents are horizontal.