Find the first and second derivatives and use them to test for maxima and minima on the given interval. Remember to check the endpoints! Homework Help ✎
y = 2 sin x + 3 cos x on [0, π]
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)
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) = _________