Question

The value of x for the minimum
value of root3 cos x+ sin x is​

Answer 1

Answer:

Step-by-step explanation:

(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:

maximum value of 3cosx+sinx is one