Question

The value of x for the maximum value of root 3cosx +sinx is

Answer 1

(x) = sqrt(3) cos x + sin x  
f'(x) = -sqrt(3) sin x + cos x = 0  
- sqrt(3) sin x = - cos x  
sqrt(3) sin x = cos x  
divide both sides by cos x  
sqrt(3) tan x = 1  
tan x = 1/sqrt(3)  

x = pi/6, 7pi/6  

f''(x) =-sqrt(3) cos x - sin x  
f''(pi/6) = -sqrt(3) sqrt(3)/2 - 1/2  
f''(pi/6) = -3/2-1/2 =-2 < 0, so f has a relative maximum at x=pi/6  
The maximum value is f(pi/6) = sqrt(3)sqrt(3)/2 + 1/2 = 2 

Answer 2

Answer:

Step-by-step explanation: