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6-63.

This problem is asking you to find EXTREME VALUES on a closed domain.
Extreme values (global maxima and global minima) can exist where y' = 0 or where y' = DNE.

Find extrema candidates where y' = 0. Remember to only consider candidates within the given domain: [0, π].
y' = 2cosx − 2sinx = 2(cosx − sinx)
0 = 2(cosx − sinx)
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Find more extrema candidates where y' = DNE. In other words, where is y non-differentiable? Are there endpoints, jumps, holes, cusps or vertical tangents? If so, these are extrema candidates. There are endpoint candidates at x = 0 and x = π.

3 extrema candidates have been identified.

Test each candidate to see who has the most extreme (highest and lowest) y-values.
The 'winners' are the global max and the global min.

y(0) = _________

y(π) = _________