An object is moving along a horizontal path with its position modeled by the equation X(t) = to - 2t - 3t, where position is measured in meters and time in seconds. What is its velocity V(t) and accelerationa(t)? ov (t) = 3t2 and a(t) = 6t - 2 ov(t) = 3t2 - 4t - 3 and a(t) = 6t - 4 O v (t) = -2t - 3 and a(t) = -2 O v (t) = 6t - 2 and a (t) = 3t2 - 2t - 3For f (X) = X4, describe the concavity of f(X). O f(x) is concave down for x 0. 0 f(x) is concave up for x 0. 0 f(x) is always concave down. O f(x) is always concave up. An object's position is described by d (t) = t3 + t2 , where d is distance in meters and t is time in seconds. "L Which of the following describe the behavior ofd " (t)? O d"(t) is positive when d(t) is concave up, t > % , and d"(t)is negative when d(t)is concave down t 0. Which of the following are true? 0 When f "(x) > 0 then f(x) is concave up and f '(x) can be either positive or negative. 0 When 1' "(x) > 0 then f(x) is concave up and f '(x) must be positive. 0 When f "(x) > 0 then f(x) is concave up and f '(x) must be negative. 0 When 1' "(x) > 0 then f(x) is concave down and f '(x) must be positive. For d(t) shown below, which of the following graphs is d "(t)? - NW -2 Not O -2 -1 1 x Not O .3 -2 -1 wot Ad w + O Not O .3 -2 -1For f(x) shown below, which of the following graphs is f "(x)? 4.8+ 3.2 1.6+ -3 -1.5 1.5 wt -1.6+ 3.2+ 4.8+ 4.8- 14.8+ 3.2+ 1.6- 116 O -3 -1.5 wt 1.5 -1.6+ O -3 -15 1.5 wt -1.6+ 3.2+ -3.2 4.8+ 4.8+ 10 4.8+ 3.2- 1.6+ O -3 Bobbit NADOC -1 2 wt O .3 1.5 1.5 wt 1.6+ .3.2+ -4.8 For the given graph of f(x); complete the table for f'(x) and f"(x). AY W - N (-1,0.5 0.5 (0.5, (1.3) (1.3,2 2.25 2.25,3 FX X 1.3) .25) f (x ) increa flat decre decre decre flat increas sing asing asing asing ing f ' (x ) negatil0 negatinegat negatio positiv O ve ve ive ve X e (-1,0.5) 0.5 (0.5, 1.3) (1.3) (1.3,2.25) 2.25 (2.25,3) f "(x) negatio negatio positi o positiv f ( x ) flat decreasing Ive ve ve e f ' (x) 0 Conc Conca Conca Conca No Conc No Conca f " (x ) negative avity we ve up ve conc ave concave up down down avity up lavity Concavity (-1,0.5 0.5 (0.5, (1.3) (1.3,2 2.25 (2.25,3 X 1.3) 25) f(x) increa flat decre decre decre flat increas sing asing asing asing ing f '(x) positiv 0 negatinegat negatio positiv le O ve live ve e f "(x) negatinegati positiv0 positi positi positiv ve ve e ve ve e