9:49 PM Tue Mar 15 Q Worksheet 10 Worksheet 8 Chapter 4 Notes 1... CHEM101 Chapter... Worksheet 10 T MATH 190 NAME : Ngozika Lilian Peter Worksheet 10 (4.1, 4.2, and 4.3) 1. For the function f(x) = In x - x, f ( x ) = 4 - 1 f" ( x ) = = 1 f' ( x ) = 0 1 -1 =0 X X = 1 0 " 2 a. identify intervals in which fis increasing b. any local extrema or decreasing decreasing => (1, 00 ) *= 1 => critical point f' co ) = 1 - 1 = ) undefined function f(x ) = Inx - x increasing = (0,1 ) = In (1) -1 Alx = 1 , fox ) has f ( 2 ) = 1 - 1 = -1 function = 0 - 1 a local maxima f' ( 2 ) = 1 =-1 f" =-1 = -1 20 c. identify intervals in which fis concave d. any inflection points up or concave down There is no inflection f " ( x ) > 0 = > cy because there is no change fox is concave down f" ( x ) CD in the curve's concavity. (01 00) f" ( x ) = - 1 f" ( 1 ) = - 1 = - 140 2. Curve sketching satisfying given conditions: a. f' (x) > 0 ifx 0 c. f" (x) > 0 ifx0 e. f(0) = 1