Page:Calculus Made Easy.pdf/99

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

Fig. 9.	Fig. 10.

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

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

Fig. 11.

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