It is shown in Exercise 5. Sec. 33. chat I . I ,') I 1 ' 00(1 -) = - Oil/ e -, e in the sense that che sec of values on chc left is lhe same as lhc sec of values on the righl. But (4) because ln(i 2) =log(- I)= (211 + 1 ):ri (11 = 0. I. 2 .... ). according to Example 3. and since 21ogi = 2 [1n I+ i (~ + 211:r )l = (411 + l):ri (I/= 0. l. 2 .... ). Upon comp
4.2 What Derivatives T ells Us I. What first derivatives tells us Increasing/Decreasing Test (I/D Test) If f ‘ > 0 on interval f is increasing on the interval If f ‘ < 0 on interval f is decreasing on the interval F is decreasing on (-5,-2) (0,5) F ‘ < 0 F is increasing on (-2,0) F ‘ > 0 Corner points f ‘ DNE o F ‘ (-2) DNE, F ‘ (0) DNE F is increasing on (-4,-3) (-1,1) f ‘ < 0 F is decreasing on (-3,-1) (2,2) f ‘ > 0 F ‘ (-3) = f ‘ (-1) = f ‘ (1) = 0 EXAMPLE 1: Sketching a function f(x) continuous on its domain (- ,) satisfying the following conditions. (1) F ‘ > 0 on (- , 0), (4,6) and (6, ) [ f increasing on (- , 0), (4,6) and (6, ) ] (2) f ‘
