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