Show in two ways that the function ln(x2 + y 2 ) is harmonic in every domain that docs not contain the origin.

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 ‘