Homework SourseFind the extrema of the function on the given interval and s
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
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
Solution
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.
