For some positive constant CC$,$ a patient$$s temperature change, TT$,$ due to a dose, DD$,$ of a drug is given by

T$=($C$2$D$3)$D$2.$T$=($C$2$D$3)$D$2.$

$(1)$ What dosage maximizes the temperature change?

$2)$ The sensitivity of the body to the drug is defined as dT$/$dDdT$/$dD$.$ What dosage maximizes sensitivity