If the curve slopes up steeper than ${\displaystyle 45^{\circ }}$ (Fig. 9), ${\displaystyle {\frac {dy}{dx}}}$ will be greater than ${\displaystyle 1}$.

Fig. 9.	Fig. 10.

If the curve slopes up very gently, as in Fig. 10, ${\displaystyle {\frac {dy}{dx}}}$ will be a fraction smaller than ${\displaystyle 1}$.

For a horizontal line, or a horizontal place in a curve, ${\displaystyle dy=0}$, and therefore ${\displaystyle {\frac {dy}{dx}}=0}$.

If a curve slopes downward, as in Fig. 11, ${\displaystyle dy}$ will be a step down, and must therefore be reckoned of