$($a$)$ Consider the function $f(t)=3^{2}2t,$ wite out the expression $\frac{f(t)-f(2)}{t-2}.$

Put $2012$

The amwer to part $($a$)$ is $\frac{3t^{2}2t-16}{t-2}.$

$($b$)$ The answer to part $($a$)$ is the arerage rate of change of $f$ on the therous $(2,f).$ The it to find the awrape rate of change of $f(t)$ on the interval $(2,2\mathrm{.}4).$

$$ the wery small interval $2,2\mathrm{.}001.$

$$