Question

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

Answer 1

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

Answer 2

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

Answer 3

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