The cubic equation y=x^3-3x^2+1 can be differentiated to obtain a formula for the slope of any tangent line to the curve.
Thid derivative is dy/dx = 3x^2-6x.
Since we're interested in finding x values at which the tangent line is horiz., we set this deriv. = to 0. Factoring, 3x(x-2)=0. Thus, x=0 and x=2.
You could verify this by graphing the original function on a graphing calculator. Determine from your graph the x-values at which the tangent lines to the graph appear to be horiz.
