DEIAILS

MY NOTES

During a certain summer thunderstorm, the temperature drops and then rises again. The rate of change of the temperature during the hour and a half after the storm began is given by

$t(h)=9\mathrm{.}36h^3-15\mathrm{.}45h^2+17\mathrm{.}34h-9\mathrm{.}89$

where output is measured in $F$ per hour and $h$ is the number of hours since the storm began.

$($a$)$ Calculate the average rate of change of temperature from $0$ to $1\mathrm{.}5$ hours after the storm began. $($Round your answer to three decimal places.$)$

$($b$)$ If the temperature was $75F$ at the time the storm began, what was the average temperature during the first $1\mathrm{.}5$ hours of the storm? $($Round your answer to three decimal places.$)$