An ornithologist determines that the body temperature of a certain bird species fluctuates over roughly a 17-hour period according to the cubic formula

for 0 ≤ t ≤ 0.713, where T is the temperature in degrees Celsius measured t days from the beginning of a period.

a. Compute and interpret the derivative T'(t).

b. At what rate is the temperature changing at the beginning of the period (t = 0) and at the end of the period (t = 0.713)? Is the temperature increasing or decreasing at each of these times?

c. At what time is the temperature not changing (neither increasing nor decreasing)? What is the bird’s temperature at this time? Interpret your result.

Transcribed Image Text:

T(t) = -68.071³+ 30.98t2 + 12.52t + 37.1 =