question_answer 1)

Find the points on the curve y = x3 at which the slope of the tangent is equal to the y-coordinate of the point. 

Answer:

Given curve is                         y = x3                            ?. (1)       Let P(h, k) be any point on (1)          K = h3                                                                  ? (2)       (1)         m = slope of tangent to (1)                   Acc. to Question                         m = K                                  ? (3)       (2) and (3) h3 = 3h2              h2 (h ? 3) = 0  h = 0, 3                  When h = 0, then            K = 0       When h = 3, then             K = 27        Required points are (0, 0) and (3, 27).