How do you find the critical points of f(x)=sinx+cosx?

1 Answer
Nghi N. ยท Maurizio Giaffredo
Apr 22, 2015

y = sin x + cos x
Use the Trig Identity sin + cos x = sqrt{2} sin (x + pi/4).
y = sqrt{2} sin (x + pi/4)
y min when sin (x + pi/4) = -1 rArr x + pi/4 = 3/2 pi rArr x = 5/4 pi.
y max when sin(x + pi/4) = 1 rArr x + pi/4 = sin pi/2 rArr x = pi/4.
In the interval (0, 2 pi) there are 2 answers: pi/4 and 5/4 pi.
Check
When x = pi/4 rArr y = sqrt{2}/2 + sqrt{2}/2 = sqrt{2} (Max)
When x = 5/4 pi rArr y = -sqrt{2}/2 - sqrt{2}/2 = - sqrt{2} (Min)

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