What are all the critical points of f(x)=sinx+cosx ? 0=<x=<2pi

Expert Answers

An illustration of the letter 'A' in a speech bubbles

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...

See
This Answer Now

Start your 48-hour free trial to unlock this answer and thousands more. Enjoy eNotes ad-free and cancel anytime.

Get 48 Hours Free Access

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).

Approved by eNotes Editorial Team