CHAPTER VIII 



70. Curves may be divided into two classes according to the 

 algebraic sign of the slope. 



(1) If y increases as x increases, then a tangent drawn to such 

 a curve will be inclined to the axis of x at an acute angle, and 



/ 

 O 



X O 



FIG. 30. 



flll 



tan will be positive and therefore -^ will be positive. Hence 



njti 



when -p, or the slope of a curve, is positive y increases as x 

 increases. 



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O 



X O 



FIG. 31. 



(2) If y decreases as x increases, then a tangent drawn to such 

 a curve will be inclined to the axis of x at an obtuse angle, and 



115 



