You found y' = 0 when x = pi. You found y"(pi) = 0 so you cannot tell whether it is a relative maximum or minimum or neither. You will have to resort to the first derivative test to determine that.
Recall that if x = c is a critical point where f'(c) = 0 and f"(c) exists , then f(x) at x = c has :
- a relative maximum if f"(c) < 0
- a relative minimum if f"(c) > 0
- if f"(c) = 0, you cannot conclude anything out of the test
This is the second derivative test.
