If a function

s left parenthesis t right parenthesiss$($t$)$

gives the position of a function at time$$ t$,$ the derivative gives the$$ velocity, that$$ is$,$

v left parenthesis t right parenthesisv$($t$)$equals$=$s prime left parenthesis t right parenthesiss$($t$).$

For the given position$$ function, find $($a$)$

v left parenthesis t right parenthesisv$($t$)$

and $($b$)$ the velocity when

tequals$=0,$

tequals$=33,$

and

tequals$=77.$

s left parenthesis t right parenthesis equals $15$ t squared minus $9$ t plus $4$s$($t$)=15$t$29$t$+4$