How do you find the maximum value of #f(x)=2sin(x)+cos(x)#?
f'=2 cos x - sin x = 0, when 2 cos x = sin x that gives
x = arc tan 2. The principal value is in Q1. Indeed, there are general
values in Q1 and Q3.
for Q3 values, as both sin x and cos x are negative in Q3.
The maximum is obtained when tan x = 2, with x in Q1. And this is
2sin x + cos x , with tan x = 2
Of course, the minimum is
Alternative method sans differentiation: