Question

Find the equations of all lines having slope 0 which are tangent to the curve y=1/(x²-2x+3).

Answer 1

The equation of the given curve is 

The slope of the tangent to the given curve at any point (x, y) is given by,

If the slope of the tangent is 0, then we have:

The equation of the tangent through  is given by,

Hence, the equation of the required line is y=1/2