${\displaystyle dx}$ will be ${\displaystyle 3}$ times as great as ${\displaystyle dy}$; as magnified in Fig. 21. So, draw the line in Fig. 20 at this slope.

(3) Now for a slightly harder case.

Let

Again the curve will start on the ${\displaystyle y}$-axis at a height ${\displaystyle b}$ above the origin.

Now differentiate. [If you have forgotten, turn back to p. 26; or, rather, don’t turn back, but think out the differentiation.]

This shows that the steepness will not be constant: it increases as ${\displaystyle x}$ increases. At the starting point ${\displaystyle P}$,