Page:Calculus Made Easy.pdf/107

 assigned value of $$x$$, the height of the ordinate in the second curve is proportional to the slope of the first curve.

If a curve comes to a sudden cusp, as in Fig. 25, the slope at that point suddenly changes from a slope



upward to a slope downward. In that case $$\dfrac{dy}{dx}$$ will clearly undergo an abrupt change from a positive to a negative value.