The following is a partial table of values for f $=$ f $($x$).($Round your answers to two decimal places.$)$

x $0246$

f $=$ f $($x$)32\mathrm{.}336\mathrm{.}040\mathrm{.}143\mathrm{.}7$

$($a$)$ Estimate the value of f $(3)$ by averaging.

$($b$)$ Find the average rate of change for f between x $=2$ and x $=4.$