;
Solution :
a)
Horizontal tangent
horizontal tangent at t = 0
corresponding point on curve is (0,-9).
Vertical tangent
vertical tangent at t =
1
corresponding points on curve are (-2,-6),(2,-6)
b)
Summary of where curve C rises and falls
From this table, we can see that when t < -1, x is increasing and y is decreasing, so the graph of y as a function of x is falling to the right. Analogous results hold on the other intervals.
The machine drawn graph confirms these statements:
by:sh