# Find the maximum value of the function f (x) = 1 + 2 sin x + 3 cos2 x , 0 = x = 2p/3.

Robin Chourasia
10 years ago
y= 1 + 2 sin x + 3 cos2x
y'= 2 cos x -6 sin 2x
y''= -2sinx-12cos2x

from y' we get,

2 cos x(1-6sinx)=0

=> x=90 or sin x= 1/6

y'' at x= 90 we get y'' = -2 - 12 (-1) = 10
at sinx = 1/6 we get y'' = -2 *1/6 -12 (1- 1/18)= -1/3- 34/3 =-35/3

Substituting both values in Y we get, @ x = 90 y = 0 @ sinx = 1/6 y = 1+ 1/3 + 3 (1-1/18)= 25/6 is maximum value..

Regards,

Robin
Parvez ali
10 years ago

Thanks & Regards
Parvez Ali

10 years ago
`f'(x)=2cosx-6cosxsinx=02cosx(1-3sinx)=0cosx=0 or sin(x)=1 f(x)=1+2=3sinx=1/3 imply cos^2(x)=1-1/9=8/9f(x)=1+2/3+3*8/9=1+10/3=4.33hence answer is 4.33.Sher MohammadB.Tech, IIT Delhi.`
bharat bajaj IIT Delhi
10 years ago
`f(x)= -3sin2x + 2sinx + 4= -3(sin2x-2/3 sinx)+ =-3(sinx-1/3)^2+3/9+4=-3(sinx - 1/3)+13/3`
`Now, for f(x) to be max, the first term should be minimum.Hence it is at sin x =0Hence, max. value of f(x) = 16/3Thanks & RegardsBharat BajajaskIITians FacultyIIT Delhi`

bharat bajaj IIT Delhi
10 years ago
`f(x)= -3sin2x + 2sinx + 4= -3(sin2x-2/3 sinx)+=-3(sinx-1/3)^2+3/9+4=-3(sinx - 1/3)+13/3`
`Now, for f(x) to be max, the first term should be minimum.Hence it is at sin x =0Hence, max. value of f(x) = 16/3Thanks & RegardsBharat BajajaskIITians FacultyIIT Delhi`

Sunil Kumar FP