Finding Maximums and Minimums
Practice Answers
Practice 1: The enrollments were relative maximums in , , and .
The global maximum was in . The enrollments were relative minimums in , , and . The global minimum occurred in .
Practice 2: is a polynomial so is differentiable for all , and . when so the only candidate for a local extreme is . Since the graph of is a parabola opening up, the point is a local minimum.
is a polynomial so is differentiable for all , and . when so the only candidates for a local extreme are and . The graph of (Fig. 22) shows that has a local maximum at and a local minimum at .
Fig. 22
Practice 3:
see Fig. 23
Fig. 23
Practice 4: (1, ) is a local minimum. is an endpoint.
(3, ) is a local minimum. is not differentiable at .
(4, ) is a local maximum. is an endpoint.
Critical points: endpoints and .