Find the extrema of the function on the given interval, and say where they occur

Question

Find the extrema of the function on the given interval, and say where they occur.
8) sin x + cos x, 0 <= x <= 2pi

A) local max: 1 at x = 2pi and 2 at x = pi/4
local min: 1 at x = 0 and - sqrt2 at x = 5pi/4
B) local max: 1 at x = 0 and - sqrt2 at x = 7pi/4
local min: 1 at x = 2pi and sqrt2 at x = pi/4
C) local max: 1 at x = 0 and - sqrt2 at x = 5pi/4
local min: 1 at x = 2pi and sqrt2 at x = pi/4
D) local max: 1 at x = 2pi and sqrt2 at x = pi/4
local min: 1 at x = 0 and - sqrt2 at x = 7pi/4

Explanation / Answer

Differeniate the equation and equate to zero to find the extremmas:- d/dx of question---> cos x - sin x =0 this is true when x=pi/4, 5pi/4, 2pi Double differentiate to find whether local maxima/minima-> d2/d2x= -sin x -cos x If negative => local maxima If positive -> local minima Clearly maxima occurs at x=0, x= pi/4 == sqrt 2 (negative at both places) and minima occurs at x= pi, x=5pi/4== -sqrt(2) (positive at both places) Ask back if you are (un)satisfied.

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