Speedometer readings for a motorcycle at 12-second intervals are given in the table

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Speedometer readings for a motorcycle at 12-second intervals are given in the table.

t (s)	0	12	24	36	48	60
v (ft/s)	30	28	25	21	25	27

(a) Estimate the distance traveled by the motorcycle during this time period using the velocities at the beginning of the time intervals.
ft

(b) Give another estimate using the velocities at the end of the time periods.
ft

(c) Are your estimates in parts (a) and (b) upper and lower estimates? Explain.

(b) is a lower estimate and (a) is an upper estimate since v is a decreasing function of t.(a) and (b) are neither lower nor upper estimates since v is neither an increasing nor decreasing function of t.    (a) is a lower estimate and (b) is an upper estimate since v is an increasing function of t.