Find the equation of the tangent line to the parabola y = x² at the point (0,0).
Let Q = ( x, x²) be another point on the graph of the parabola y = x² . The slope of the line joining (0, 0) and (x, x²) is m=\frac{x^{2}-0}{x-0}=\frac{x^{2}}{x}=x,x\neq0\;. As Q approaches (0, 0) ,x approaches 0, and the slope approaches 0. Hence the slope of the tangent line is 0, and the equation becomes y – 0 = 0 (x – 0), or y = 0. The tangent line is horizontal!