Find dy/dx by implicit differentiation. Then find the slope of the graph at the given point.

Question

xy = 12, (-2, -6)

(a) dy/dx= ?

(b) At (-2,-6): y' = ?

Answer 1

(a) xy = 12. We differentiate implicitly: y + xy'/ = 0; dy/dx = y' = - y/x;

(b) Slope of graph at point (- 2, - 6) m = - (-6/(- 2)) = - 3