Question

6. Find the critical numbers and the open intervals on which each of the following functions is increasing or decreasing. a. f(x) = b. f(x) = x3 – 12x c. f(x) = x ) = x2/3 –4 X x2 + 9

Answer 1

Gras FORDEN lara For critical numbers f'(x)=0 flas=d da (Letra) (279) (2) -2 (279) (229) fla) = (x29 (1) - 2 (20) f(x) = arg-20² (1%eg? f(x) = -2²79 (leg f(x)=0= -x79 20 2²=-9 2²9 a=13 critical numbers are 125-3,3 Function is in creasing when fl(a) 70 1-е -29 20 (9) -*+970 -227-9 2 -35a<3 Increasing interval (-3, 3) Femction is decreasing when f(x20 -2²4920 x²29 2 x<t3 72-3, 2>3

Inteswal of decreasing: 600,-3) V(8,00) b f(x) = 2120 floro 30²_12 zo 30²=12 a²=4 u=$2 Critical numbers are a=-2,2 Increasing: floa) 20 80²-1270 22-470 x²>4 a>£2. az- 2x32 Intewal of increasing : 600,-2) U (2400) decreasing: FOUCO 30²_1220 x²_440 x²24 a<£2 ) -22022 Intewal of decreasing: (-2,2) 6© FO) = 24 8.68 f(x) = 2x 48-1 floga za neke

48 250 N20 - critical primber=2=0 Increasing f (2) 70 23 28 70 2370 Interval of increasing: 6,00) decreasing flaco 23 20 azo Intewal of decreasing = (-00,0)