Chapter 10.5, Problem 99E

(a)

To determine

To graph: The derivative of the function $c\left(t\right)=-0.0012t^3+0.12t^2-1.83t+3.97$, $20\le t\le 50$ by technology and then choose the correct option for the behavior of $c^{\prime }$ in interval $\left[20,32\right]$, where C is the function of time t (in days) which represents the consumption of oxygen by a turkey embryo in milliliters per hour. The consumption of oxygen increases with time as egg is laid to the time it will hatch that is approximately $t=50$.

The options are:

(A) Increasing, then decreasing

(B) Decreasing then increasing

(C) Decreasing

(D) Increasing

(b)

To determine

The derivative of the function $c\left(t\right)=-0.0012t^3+0.12t^2-1.83t+3.97$, $20\le t\le 50$ using $\text{TI-}83$ calculator and then use the graph to determine the day when the most rapid of increase of oxygen, where C is the function of time t (in days) which represents the consumption of oxygen by a turkey embryo in milliliters per hour. The consumption of oxygen increases with time as egg is laid to the time it will hatch that is approximately $t=50$.

(c)

To determine

The day when the slowest of increase of oxygen of function $c\left(t\right)=-0.0012t^3+0.12t^2-1.83t+3.97$, where C is the function of time t (in days) which represents the consumption of oxygen by a turkey embryo in milliliters per hour. The consumption of oxygen increases with time as egg is laid to the time it will hatch that is approximately $t=50$.