Answer Happy

4. The number of hours of daylight varies throughout the course
of a year (daylight is defined as the time between sunrise and
sunset). It has been suggested to approximate the length of
daylight in Maths city by the function:
,,
0 ≤ 𝑡 ≤ 365, where 𝑓(𝑡) is the number of daylight hours, 𝑡 is time
measured in days (𝑡 = 0 at January 1, 2022), and radian angle
measure is used. a = 10, b = 6 , c = 11
(a) What is the lengths of daylight when 𝑡 = 0 and 𝑡 = 𝑎 + 𝑏 − 𝑐
+ 200?
(b) What is the shortest length of daylight? What is the value
of 𝑡 then?
(c) What is the longest length of daylight? What is the value of
𝑡 then?
(d) Find the domain and range of the function using interval
notation.
(e) Use the information from (𝑎) − (𝑑) to sketch a graph of the
function, including all relevant information.
(f) Find 𝑓′′(𝑡) (the second derivative of 𝑓(𝑡)).