1 (min) 0 5 10 15 20 25 30 35 40 45 50 v(1) (km/min) 1.5 1.8 23 24 1.8 1.3 0.8 0.3 0 -0.4 -1.2 6.
A car drives on a straight road with a positive velocity vét), in kilometers per minute at timet minutes. The table above gives selected values of v(t) for Osts 50. The function v(t) is a twice-differentiable function of t.
(a) For 0<< < 50, must there be a time t when v(t) = -1 ? Justify your answer.
(b) Based on the values in the table, what is the smallest number of instances at which the acceleration of the car could equal zero in the open interval 0<=<50? Justify your answer.
(c) At what values of x does f(x)= (x-1) (3-x) have the absolute maximum?
(A) 1 (B)3/2 (C) 2 (D)5/2
(d) At what value of x does f(x)= x - 2x^2% have a relative minimum?
(A)64/27 (B)16/9 (c)4/3 (D) 2
