### Home > CALC > Chapter 6 > Lesson 6.2.1 > Problem 6-63

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*' = 2cos*x* − 2sin*x* = 2(cos*x* − sin*x*)

0 = 2(cos*x* − sin*x*)

[show steps]

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) = _________