Question

Determine the open intervals on which the graph is concave upward or concave downward, (Enter your answers using interval notation, If an answer does not exist, enter DNE.) 19 x) concave upward concave downward

Answer 1

f(x) = 15 x2+3 If f" (070 then f is concave upsword. If f"w.so then f concave downward. find flies flow = (x+3):d(19) - 19 dra?+3) (22+3)2 0-19 (22) (2+3) = -388 (x²+3) e equate it to rew -382 =0 + x =0 f'(x) = d (-380) (x2+32 Ca2+372 (-38) – 6-382) (2 622+3):20). (22+374 - (62+3) 6-38) +38x (42 (22+3) = -38%2_114 + 15282 (2x2+3)3

114X² is Cor?+3)3 ___ = 114 ( 7?,7 (x²+373 Compon f(n) to zero 14(x²1)=0 ?120 xx=1 &x =-1 divide the real number line wing x=142=1 So be get inte grade - (-co-1) (A, 12 & 0,0) Check the sign of f" (Q) on each abou interval Interval. 60,-1) Bigo.etf | Positive (tre) Son cavity Concave up. (1,1 - (negatiu) Concan down. C1,0) Politin (tv) I Concave up Concax Upword - (-6) UCLO) Concave down worda (1,1)