f(t) = -2t2+ 16t describes the distance that a ball has traveled in meters per second. What is the average rate of change of the ball between t = 1 seconds and t = 3 seconds? O Average rate of change between t = 1 and t = 3 is -2 m/s. O Average rate of change between t = 1 and t = 3 is 2 m/s. O Average rate of change between t = 1 and t = 3 is -8 m/s. O Average rate of change between t = 1 and t = 3 is 8 m/s.Assume that a rectangle with sides )1 and y is expanding with time. Let y = 3x and x(t) = 4t + 1. What is the formula for the rate of change of the area with respect to time? 0 : 2(41 + 1) o E : 8(4t + 1) 0 : 24(41 1) 0 : 16(4t 1) A square with side x cm, is changing with time where x(t) = 4t - 2. What is the rate of change of the area of the square when t = 3 seconds? O dA = 80 cm/sec dt O dA = 96 cm/sec dt O dA = 72 cm/sec dt O d.A = 10 cm/sec dtf(t) = -t2 + 10t describes the distance that a ball has traveled in meters per second. What is the average rate of change of the ball between t = 2 seconds and t = 4 seconds? O Average rate of change between t = 2 and t = 4 is 2 m/s. O Average rate of change between t = 2 and t = 4 is -4 m/s. O Average rate of change between t = 2 and t = 4 is -2 m/s. O Average rate of change between t = 2 and t = 4 is 4 m/s.Assume that a rectangle with sides x and y is changing with time. Let y = 3x and x(t) = 2t?. What is the rate of change of the area at time t = 2? O dA = 48 dt O dA = 384 dt O dA 96 dt O dA dt = 192A track athlete is preparing to throw the javelin in competition. The javelin is thrown at time t = 0 and lands at time t = 3. Can Rolle's Theorem be applied to show that at some point between t = 0 and t = 3, the javelin has achieved a maximum and or minimum speed? O The conditions of Rolle's Theorem are met and Rolle's Theorem does state that you can find min or max points. The conditions of Rolle's Theorem are not met and Rolle's Theorem does not state that you can find min or max points. O The conditions of Rolle's Theorem are met and Rolle's Theorem does not state that you can find min or max points. O The conditions of Rolle's Theorem are not met and Rolle's Theorem does state that you can find min or max points.A cube is shown with all sides equal to x. Let x change with respect to tsuch that x(t) = 3t. I What is the formula for the rate of change of the volume of the cube? 0 The rate of change of V(t) is V'(t} = 9?. O The rate of change of V(t) is V'(t} = -9t2. O The rate of change of lt) is V'(t} = 81?. O The rate of change of V(t) is V'(t} = 9?. What function should be used to minimize the distance between y = 2x3 and the point [0, 2)? 0 13(3) = \\/ (:1: _ 2)2 +(21c3 _ 0)2 3(3) = \\/ (:1: (1)2 _ (23:3 2f 0 13(3) : (a: (1)2 ($3 2)? 0 13(3) 2 (a: _ 2)2 + (2:123 _ (1)2 The triangle shown has base b and height h. h b Assume that 2b + h = 36 to find the maximum area of the triangle? O A = 243 O A = 162 O A = 81 O A = 40.5Given the right triangle ehewn, x + y = 25. I What formula will maximize the area of the triangle 0 A : a:(25 at) 0 A : a:(25 + 3:) 0 A = $2395 :12) O A: %a:(25+:r:)