Page:Calculus Made Easy.pdf/99

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

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 $$\frac {dy}{dx}=0$$.



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