Mathematics

Problem

An object moves along a straight line with displacement (in meters) given by

s(t)=t^{4}e^{-t}

for

t\ge0

seconds. At which of the following times does the graph of

s

have a point of inflection? a)

t=2\text{ s only}

t=0\text{ s and }4\text{ s}

t=2\text{ s and }6\text{ s}

t=0\text{ s},\;2\text{ s},\text{ and }6\text{ s}