Assume MATH 12 Students' happiness function is given by H = C2Q + 2E
Where,
H is the students' happiness
C is the students' happiness due to going to Math 12 class
Q is the students' happiness due to taking Math 12 Quizzes
E is the students' happiness dues to taking Math 12 Exams
Assume that at the end of the semester:
1. Students' happiness due to going to class is 5 utils/week, and is decreasing by 2 utils/week.
2. Students' happiness due to taking Math 12 Quizzes is 10 utils/week, and decreasing by 1 util/week.
3. Students' happiness due to taking the Exams is 2 utils/week and is decreasing by 1 util/week.
QUESTION: By how much is Students' happiness increasing/decreasing at the end of the quarter. (Note: This problem does not correspond to reality) HINT: Use implicit differentiation with respect to time.