+52 A series of locks manages the water height along a water source used to produce energy. As the locks are opened and closed, the water height between two consecutive locks fluctuates.
The height of the water at point B located between two locks is observed. Water height measurements are made every 10 minutes beginning at 8:00 a.m.
It is determined that the height of the water at B can be modeled by the function f(x)=−12cos(πx32−7π8)+30, where the height of water is measured in feet and x is measured in minutes.
What is the maximum and minimum water height at B, and when do these heights first occur?
