Suppose that $f(t)=t^{2}t-4.$

$($a$)$ What is the average rate of change of $f(t)$ over the interval $1$ to $2?$

$($b$)$ What is the $($instantaneous$)$ rate of change of $f(t)$ when $t=1?$

The average rate of change of $f(t)$ over the interval $1$ to $2$ is $4.$

$($Simplify your answer.$)$

The $($instantaneous$)$ rate of change of $f(t)$ when $t=1$ is $3.$

$($Simplify your answer.$)$