# How do you find the maximum value of #f(x)=2sin(x)+cos(x)#?

##### 1 Answer

Sep 1, 2016

Range is

#### Explanation:

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: