Chapter 3.5, Problem 100E

Embryo Development The oxygen consumption of a galliform bird embryo increases from the time the chick hatches. In a typical galliform bird the oxygen consumption (in milliliters per hour) can be approximated by

$c\left(t\right)=-0.0027t^3+0.14t^2-0.83t+0.15\left(8\le t\le 30\right),$ wheret is the time (in days) since the egg was laid. (An egg will typically hatch at around $t=28$.) Use technology to graph $c\text{'}\left(t\right)$, and use your graph to answer the following questions. [HINT: See Example 5.]

a. Over the interval $\left[8,30\right]$ the derivative $c\text{'}$

is

(A) increasing, then decreasing.

(B) decreasing, then increasing.

(C) decreasing.

(D) increasing.

b. When, to the nearest day, is the oxygen consumption increasing the fastest?

c. When, to the nearest day, is the oxygen consumption increasing at the slowest rate?