Counting the brackets, I will assume you meant
T(t)=50+14Sin((pi(t))/12)
besides that would make the period 24 hours, which makes sense
since t = 0 corresponds with 9:00 am
the temp at 9:00 am was 50°
9:00 am to 9:00 pm is 12 hours.
the min will be 50 - 14 = 36
and the max will be 50+14 = 64° <--- at 3:00 pm , t = 6
in a certain city the temperature (in degrees fahrenheit) to hours after 9am was modeled by T(t)=50+14Sin((pi(t))/12. Find the highest temperature during the period from 9AM to 9PM. Indicate units
3 answers
What is the derivative of T(t)=50+14Sin((pi(t))/12)?
We are able to use a calculator but I keep getting different answers because I think Im not sure how to get the derivative on the calculator
We are able to use a calculator but I keep getting different answers because I think Im not sure how to get the derivative on the calculator
There is really no need to actually use Calculus for this.
You asked for the max.
sin(??) runs from -1 to +1
so 14Sin((pi(t))/12) has a max of 14(1) = 14
and the max of T(t) = 50+14 = 64
however, if you want to use Calculus
T'(t) = 14cos(((π(t))/12)(π/12) = (14π/12) cos (((π(t))/12) = 0 for a max/min
cos (((π(t))/12) = 0
π(t)/12 = π/2 , 3π/2
t = 6 or t = 18
sub t = 6 into the original to get 64 , the max
sub t = 18 into the original to get 36, the min
You asked for the max.
sin(??) runs from -1 to +1
so 14Sin((pi(t))/12) has a max of 14(1) = 14
and the max of T(t) = 50+14 = 64
however, if you want to use Calculus
T'(t) = 14cos(((π(t))/12)(π/12) = (14π/12) cos (((π(t))/12) = 0 for a max/min
cos (((π(t))/12) = 0
π(t)/12 = π/2 , 3π/2
t = 6 or t = 18
sub t = 6 into the original to get 64 , the max
sub t = 18 into the original to get 36, the min