Answer :
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
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
