Find the absolute extreme values of y=cos(x) + sin(x) on the interval 0 to 2pi
y'=cos(x) - sin(x)
y'=0 when x= pi/4
However, the answer in the book is max: sqrt{2} min: -sqrt{2)
P.S. Is it just me or am I getting a latex error?
Find the absolute extreme values of y=cos(x) + sin(x) on the interval 0 to 2pi
y'=cos(x) - sin(x)
y'=0 when x= pi/4
However, the answer in the book is max: sqrt{2} min: -sqrt{2)
P.S. Is it just me or am I getting a latex error?
Hi
You don't need to take the derivative
y=cos(x) + sin(x)=sqrt(2) (sqrt(2)/2 . cos(x) + sqrt(2)/2 . sin(x)) = sqrt(2) (sin(pi/4) . cos(x) + cos(pi/4) . sin(x)) = sqrt(2) sin(x+pi/4)
Otherwise with the derivative
y'=cos(x) - sin(x)
y'=0 when x= pi/4 (mod 2pi) or x=5pi/4 (mod 2pi)
y(pi/4) = sqrt(2)
y(5pi/4) = -sqrt(2)
The problem is known. Admins are trying to fix it.