The critical points are determined by differentiating the function and equating the derivative to 0. It is solved to determine x.

f(x) = sin x + cos x

f'(x) = cos x - sin x = 0

=> cos x = sin x

=> tan x = 1

=> x = arc tan 1

=> x = pi/4 , 5*pi/4

At x = pi/4 , f(x) = sqrt 2

at x = 5*pi/4, f(x) = -sqrt 2

**The critical points are at x = pi/4 and x = 5*pi/4, and the extreme values are (pi/4, sqrt 2) and (5*pi/4,-sqrt 2).**

## We’ll help your grades soar

Start your 48-hour free trial and unlock all the summaries, Q&A, and analyses you need to get better grades now.

- 30,000+ book summaries
- 20% study tools discount
- Ad-free content
- PDF downloads
- 300,000+ answers
- 5-star customer support

Already a member? Log in here.

Are you a teacher? Sign up now