College board
the number of hours of daylight, d, in hartsville can be modeled by d = (35/3) + (7/3) (sin((2π/365) where t is the number of days after march 21. the day with the greatest number of hours of daylight has how many more daylight hours than may 1? (march and may have 31 days each. april and june have 30 days each.)
a. 0.8 hr
b. 1.5 hr
c. 2.3 hr
d. 3.0 hr
e. 4.7 hr

Since this is an SAT Math Level 2 problem derivatives should not be required to find the solution. To find "How many more hours of daylight does the day with max sunlight have than May 1," all you need to understand is that sin(x) has a maximum value of 1.

The day with max sunlight will occur when sin(2*pi*t/365) = 1, giving the max sunlight to be 35/3 + 7/3 = 14 hours

Evaluating your equation for sunlight when t = 41, May 1 will have about 13.18 hours of sunlight.

The difference is about 0.82 hours of sunlight.

Even though it is unnecessary for this problem, finding the actual max sunlight day can be done by solving for t when d = 14, of by the use of calculus. Common min/max problems on the SAT Math Level 2 involve sin and cos, which both have min values of -1 and max values of 1, and also polynomial functions with only even powered variables or variable expressions, which have a min/max when the variable or variable expression equals 0.

For example, f(x) = (x-2)^4 + 4 will have a min value of 4 when x = 2. Hope this helps