(c) The functions

x(t)^(3)

and

t^(3)

are functions. Therefore, so long as

d(x)/(d)t=t^(3)-x(t)^(3),0x(t)t_(0)=2.5,x(t_(0))=2t>2.5,x(t)x=1x(t)^(3), and d(x)/(d)t=t^(3)-x(t)^(3),0 meaning that x(t)\ At the initial point t_(0)=2.5,x(t_(0))=2, which is less than 2.5. Therefore, if t>2.5,x(t) cannot take values than 2, and the parificle reach the location x=1.x(t), then x(t)^(3), and d(x)/(d)t=t^(3)-x(t)^(3),0 meaning that x(t)\ At the initial point t_(0)=2.5,x(t_(0))=2, which is less than 2.5. Therefore, if t>2.5,x(t) cannot take values than 2, and the parificle reach the location x=1.

(c) The functions x(t)3 and t3 are functions. Therefore, so long as x(t)2.5,x(t) cannot take values than 2 , and the parificle reach the location x=1