7

�U�@��: 8 �W�@��: �G�B�h��D �e�@��: 6

7

�] f'(x) ��ܹ�Y�Ʀh�� f (x) ��ɨ�ơA�w�� y = f'(x) ��ϧάO�@�ӳq�L�I (1, 0) �M�I (2, 0) �B�}�f�V�W��ߪ��u�C�հݤU�C��ǿﶵ�O��T��H

(1) f (x) �@�w�O�T��h�� (2) f (x) �b 1 < x < 2 ��d�򤺥��W

(3) f (x) �@�w�꦳��ӷ�� (4) f (x) = 0 �@�w��T�ӹ��

(5) f (x) = 0 �b 1 $\le$ x $\le$ 2 ��d�򤺤@�w��

��:��D�O�Q�ξɨ�ƪ��ϧΨӧPŪ��ƪ��ϧ�, �򥻤W�u�n�F�Ѿɨ�ƪ��t��ȩM��ƪ��W����Y�H�ξɨ�ƵL�k�M�w��ƪ��ȳo��ӷ��N��D. ��D�ﶵ (4) �M�ﶵ (5) �ݪ��O�P�@�ӷ��, ��O�F�@�ӿﶵ��I�i��.

�ڭ̱q�D�ص�� f'(x) ��T��ۤ�. ��D�N y = f'(x) ��ϧΦp�U:

$\begin{picture}(170,124)(0,6) \thinlines\drawpath{16.0}{120.0}{16.0}{4.0}\drawce... ...,92.16) \path(143.58,92.16)(143.78,93.08)(144.0,93.98)(144.0,94.0) \end{picture}$

�� y = f'(x) ��ϧάO�ߪ��u�� f'(x) �O�@�ӤG��h��, �G�o�� f (x) ��@�ӤT��h��. ��ۥ� y = f'(x) �q�L (1, 0) �M (2, 0) �� f'(1) = 0 �B f'(2) = 0. �A�� y = f'(x) �O�}�f�V�W��ߪ��u�� 1 < x < 2 �� f'(x) < 0; �ӷ� x < 1 �� x > 2 �� f'(x) > 0. �Ѧ�� f (x) �b 1 < x < 2 ��d�򤺬��; �� f (x) �b x < 1 �� x > 2 ��d�򤺬��W. �̦��ڭ̤]�i�o�� f (x) �Ȧ��b x = 1 �M x = 2 �ɦ��. �ƹ�W f (x) �b x = 1 ��j��, �Ӧb x = 1 ��p��. �ڭ̥i�H��e�X y = f (x) ��ϧΦp�U:

$\begin{picture}(80,80)(0,20) \thinlines\path(60.0,58.0)(60.0,58.0)(59.62,58.81)(... ...{44.0}{26.0}{\tiny$x=1$} \drawcenteredtext{76.0}{26.0}{\tiny$x=2$} \end{picture}$

�j�a��D�� c �O�@�ӱ`�Ʈ�, g(x) = f (x) + c ��ɨ�ƩM f (x) ��ɨ�ƬO�ۦP�� (��p��D�� f'(x) �]��w), �ҥH�W�Ϥ��ڭ̵L�k�M�w x �b��m. �]�N�O��ﶵ (4) �M�ﶵ (5) ��O��. �ƹ�ѤW��ϧΧڭ̪��D��ݪ� f (1) $\ge$ 0 �B f (2) $\le$ 0 ��T�O f (x) = 0 ��T��, �]�u��b�o��p�~��T�O f (x) = 0 �b 1 $\le$ x $\le$ 2 ��.

��D�ڭ̤]�i�� f'(x) = r(x - 1)(x - 2), �䤤 r ��@�� (�] f'(1) = f'(2) = 0 �B y = f'(x) �ϧά��}�f�V�W��ߪ��u), �Q�ΤϾɨ�Ʊo f (x) = (r/3)x³ - (3r/2)x² + 2rx + c. �A��X�ϨҪ��ﶵ (4), (5) ��O��. �Ҧp�� r = 6 �B c = - 6 ��, f (x) = 2x³ - 9x² + 12x - 6. �� f (x) = 0 �Ȧ��@��ڥB��ڤj�� 2 (�] f (1) < 0).

�U�@��: 8 �W�@��: �G�B�h��D �e�@��: 6

Li 2008-08-16