1. ## Application of derivative

It's really a long question, plz help me solve this probem!~thanks a lot!~

The eating behavior of a typical human during a meal can be described by
I(t)=27+72t-1.5tsquar.

where t is the number of minutes since the meal began and I(t)represents the amount(in grams) that the person has eaten at time t.

a)find the rate of change of the intake of food for this particular person 5 minutes into a meal and interpret.

b)verify that the rate in which food is consumed is zero 24 minutes after the meal starts.

c)comment on the assumptions and usefulness of this function after 24 minutes.Given this fact,determine a logical domain for this function.

2. Originally Posted by shannon1111
It's really a long question, plz help me solve this probem!~thanks a lot!~

The eating behavior of a typical human during a meal can be described by
I(t)=27+72t-1.5tsquar.

where t is the number of minutes since the meal began and I(t)represents the amount(in grams) that the person has eaten at time t.

a)find the rate of change of the intake of food for this particular person 5 minutes into a meal and interpret.
You have $I(t) =27 + 72 t - 1.5t^2$
Compute $I'(t)$ and then $I'(5)$ for your answer.
To find derivative remind yourself the exponent rule.

b)verify that the rate in which food is consumed is zero 24 minutes after the meal starts.
Using same as above show $I'(24)=0$.