\f0 Question 9 v Suppose that the position of a particle is given by s = it) = 4t3 + 7t + 9. (a) Find the velocity at time t. m 1; t = l ) l s (b) Find the velocity at time t = 3 seconds. m s (c) Find the acceleration at time t. m 01*) =' g (d) Find the acceleration at time t = 3 seconds. m 32 Check Answer 0 Question 10 v Given the function g(:1:) = 4:123 + 6:32 1443:, find the first derivative, g'(m). 91$)=\\ \\ Notice that g'(a:) = 0 when :1: = 4, that is, g'(4) = 0. Now, we want to know whether there is a local minimum or local maximum at m = 4, so we will use the second derivative test. Find the second derivative, 9\" (11:) gw)=\\ ' Evaluate g\"(4). ET4)= Based on the sign of this number, does this mean the graph of 9(3) is concave up or concave down at a: = 4? [Answer either up or down -- watch your spellingll] At a: = 4 the graph of 9(m) is concave Based on the concavity of g(cc) at :1: = 4, does this mean that there is a local minimum or local maximum at a: = 4? [Answer either minimum or maximum -- watch your spelling! !] At a: = 4 there is a local Check Answer 0 Question 11 v A piece of cardboard measuring 10 inches by 11 inches is formed into an open-top box by cutting squares with side length a: from each corner and folding up the sides. Find a formula for the volume of the box in terms of :1: We) =l l Find the value for a: that will maximize the volume of the box w=l l Check Answer 0 Question 12 v Suppose that 3:4 + y4 = 82. d (1) Use the method of implicit differentiation to find dy' :1: =' do: {2) Find the equation of the tangent line at the point (m, y) = (3, 1). The equation is y = ' Check Answer 0 Question 13 v Speedometer readings for a vehicle {in motion) at 8-second intervals are given in the table. t (sec) v (ftis) 0 25 8 28 16 17 24 31 32 26 40 24 Estimate the distance traveled by the vehicle during this 40-second period using the velocities at the beginning of the time intervals. distance traveled m feet Give another estimate using the velocities at the end of the time periods. distance traveled 3 feet Check Answer 0 Question 14 v Evaluate the definite integral by interpreting it in terms of areas. -/:(5:I: 25)da: \\ Check